To clarify. I am aware that being a Mage is not genetic and biologically speaking Mages are no different from humans(At least they aren't unless they modified their bodies. ) but Mages inflict their brand of magick on the world passively with the amount they are inflicting increasing along with their level of power. (Eventually reaching a degree where just staying in reality is a source of paradox) But does the resonance cause their kids to display traits related to the resonance whether it be in the form of turning them into a source of resonance themselves or giving them exceptional traits such as incredible creativity or being able to 'talk' to computers?
Are there any records of a child born from Mages possessing strange quirks or thestical powers
mage-the-ascensionworld-of-darkness
Related Solutions
There was a Thaumaturgy ritual on the old Vampire Players guide (and I believe in some old edition of Dark Ages) that can do specifically that.
Binding the Beast (Level Four Ritual)
This powerful ritual will pull a fellow kindred out of frenzy and even separate the vampire from his Beast for a time. The ritual takes only 10 minutes to perform, and the caster does not have to see the subject, but he must imbibe a full Blood Point of the frenzied character's blood (it can have been drawn earlier) and push an iron spike through his own hand (causing two Health Levels of damage that can't be soaked). Upon completion of these acts, the subject suddenly emerges from frenzy, and often becomes uncharacteristically passive.
In truth, his bestial side has been separated from his psyche for a number of nights equal to the number of successes the caster scores on a Manipulation + Empathy roll (difficulty of 10 minus the subject's Humanity). During this time, the subject cannot frenzy, cannot regain Willpower, can only use one Blood Point per turn regardless of generation, and cannot even feed without making a Courage roll. In addition, the vampire must make a Willpower roll (difficulty 7) to use any Discipline. Legend states that some Kindred have starved into torpor after having been subjected to this ritual. The subject doesn't need to be in a frenzy, nor does she need to be willing, but the caster may never use this ritual on himself.
Exact place where you can find this ritual is on Vampire the Dark Ages Core Rulebook (Revised Edition) pages 170-171 (although the wording on that one isn´t exactly as my quoted text).
Technocrats have a mix of advantages and disadvantages compared to other Mages.
The first, and most obvious, difference between Technocrats and other Mages is that they have access to the variant Technocratic Spheres - they can choose to learn Dimensional Science instead of Spirit, Primal Utility instead of Prime, and Data instead of Correspondence. These aren't mandatory - many Void Engineers learn Correspondence rather than Data, for instance, since the former is a lot more useful in both outer space and alternate dimensions - but Technocrats simply have options that other Mages don't.
Secondly, when they have access to Technocratic manufacturing facilities, they can manufacture Devices and other permanent Wonders without needing to invest a point of permament Willpower into each Wonder. This is mentioned in the Wonder-creation chapter of the Book of Secrets.
Thirdly, they are incapable of transcending the use of Tools in their Foci like other Mages; this is mentioned in the chapter on Foci in the M20 corebook. A possible exception is if they have taken the Psychic Practice from M20 Book of Secrets as one of the three Practices in their Focus; it says in the listing of that Practice that technomancers who have it can transcend Tools when working with that Practice as though they were mystic Mages, but whether or not that applies to Technocrats or just non-Technocratic technomages is ambiguous.
It should be pointed out, however, that Technocrats are fully capable of the full breadth of spontaneous magick granted by their Spheres with the use of their Practices and Tools - whether that is them unlocking prototype functionality in their equipment, building prototype devices, utilising advanced techniques from their martial arts training, running an app on their cell phone, etc. They're not reliant on premade Gadgets and Devices; they just can't cast Magick without one of their Tools.
Finally, Technocrats have access to certain Backgrounds that non-Technocrats don't have access to, but that's more a function of their organisation and its resources than of their magick. Similarly, some of their game traits have different names, but that's simply a matter of their culture giving different names to the same game-mechanical traits - a Mage's magical energy works just the same regardless of whether it's called Quintessence, Primal Energy, or Qi.
Best Answer
It depends on your definition of born
The most strange mages are sometimes not the traditions, but the technocrats. Among them, biomodding, aka "organic enhancement" is a well-honored tradition, especially among the Progenitors. And among their lines... Well, let's say that beings created in their labs are not necessarily what you'd expect from what is written on their file as base material. And here comes in what I said in the header: It depends on what you define as born. So, let's look at different ways to use the word born:
File #[Redacted]: Common “Steelskin” Cyborg - Reborn/Remade
As described in M20, Appendix I: Allies and Antagonists, p.623, these are more or less reborn in a lab under Progenitor oversight. They are conditioned, trained, and have a fragment of personality. But they also most likely have a totally different body structure, so you wouldn't recognize Peter, the clerk from your local bank, after he has been turned into Project 1234.
File #[Redacted]: Bioenhanced Field Agent - Reborn/Remade
As described in M20 Gods & Monsters, Chapter One: Sleepers, Consors, Hunters, and Night-Folk, p.51, Progenitors run bio-enhancement schemes on their field agents even in a limited fashion. The products of these projects are very akin to Captain America or other superheroes that acquired their powers after birth.
File #[Redacted]: Enlightened Shock Corps & Atlas Units - Reborn/Remade
As described in M20 Gods & Monsters, Chapter Two: Constructs and Familiars, p.82, the goal of the Atlas Units was to turn Traditionalists into cybernetically enhanced helpers for the Technocracy. It had some success, but the project went... haywire. It's discontinued and some of the results became HIT Marks.
File #[Redacted]: HIT Mark - Reborn/Remade or made that way
As described in M20, Appendix I: Allies and Antagonists, p.624, Iteration X is one of the best customers when it comes to HIT Marks. M20 Gods & Monsters, Chapter Two: Constructs and Familiars, p.82 there are many many models of them. These cybernetically and genetically modified humanoids (some have been Mages before subjection to this) might or might not use stock from Progenitor labs, making it possibly hard to place them on the categories of born.
File #[Redacted]: Project Victor - made that way
As described in M20, Appendix I: Allies and Antagonists, p.624, Project Victor, or Homo superior is the pinnacle of Bodymodification and genetic engineering. They are of the grown in a lab type, so are best considered born that way, though they do get augmented after birth and during training.
File #[Redacted]: Igors - Born or reborn/remade?
As described in M20 Gods & Monsters, Chapter One: Sleepers, Consors, Hunters, and Night-Folk, p.41, Igors are a time-honored tradition among the Traditions to take on helpers, that are different. Some of these are offspring of a whole lineage of such Igors, making it hard to distinguish if they are modified after birth or if their predisposition is an inheritable trait that was given to them generations ago.
File #[Redacted]: Robots & artificial beings - made that way
As described in M20 Gods & Monsters, Chapter Two: Constructs and Familiars, p.78, Some mages go the extra mile to create their own offspring from scratch. They are different. Like Darius, the Hologram adult toy. Or Masako 01, a doll-child made by an Etherist.
File #[Redacted]: Reanimates - Reborn/Remade or Made that way
As described in M20 Gods & Monsters, Chapter Two: Constructs and Familiars, p.85, some mages use dead to create beings that are no longer dead. Some of them are plain out reanimation, others are body horrors, such as Eye Scream. But Frankenstein's creation also counts and is even described in detail, and he was aimed to be the perfect companion by Doctor Frankenstein! Can you say those are anything but the children of their creators?
File #[Redacted]: Genetic Defects - Born naturally
As described in M20, Appendix II: Odd Ends, p.648, Genetic Flaws are a thing. Now, some mages, especially those that undergo a lot of bio-modding or mind sculpting, can result in giving their offspring the same or similar traits.
Nature v Nurture
While all above is the (modified) nature of beings, a lot of traits are actually trained and learned. Nurture. Especially among the Hermetic Order, it was a long time common to have non-awakened offspring of mages be indoctrinated in Hedgemagic. This however is nurture and training. See also: M20 Sorcerer for this.