Our use case spell will be inflict wounds (available to evil divine soul sorcerer):
Make a melee spell attack against a creature you can reach. On a hit, the target takes 3d10 necrotic damage.
The sorcerer's metamagic distant spell says:
When you cast a spell that has a range of touch, you can spend 1 sorcery point to make the range of the spell 30 feet.
This answer argues that the phrase "you can reach" should not prevent inflict wounds modified by distant spell from affecting a target outside of our touch range. We will assume as the user Blckknght writes:
Most touch-ranged spells refer to touching the target in their descriptions, so if the clause of the metamagic is to mean anything, it needs to override the relevant part of the description as well as the range section of the spell stats.
The feat Spell Sniper says:
When you cast a spell that requires you to make an attack roll, the spell's range is doubled.
Would Spell Sniper working together with distant spell allow us to cast inflict wounds on a target up to 60 feet away?
This answer states in passing that this would be the case, but the answers to this question seem to argue that Spell Sniper is taken into consideration before the distant spell metamagic is applied.
Best Answer
60 Feet is Correct
I think some of your confusion on this is coming from the notion that the defined range of Touch for Inflict Wounds is somehow a static distance in feet. This is not the case, per the basic rules, it's just what can you touch.
So to that end, assume you're somehow a creature with a natural reach greater than 5' and a Spellcasting feature that lets you cast spells with a range of Touch. In that scenario you can affect things further away subject to that reach. So if you're a Roper that somehow has spellcasting, you could affect creatures 50' away with touch spells.
So with that in mind, using your Metamagic to change the range of the Touch spell to one that has a fixed distance of 30' is acceptable. From there, you are now casting a spell with an attack roll and a spell's range that can be doubled (30' from the Metamagic).
Thus, this Sorcerer can cast Inflict Wounds from 60' away.