As @KhadaKuraki mentions, +X foci don’t really exist, but it seems sensible that a paladin, especially one worshiping a god who is centered on swords, might have their sword function as the holy symbol equivalent of a wand of the war mage.
Personally, I would do that – but it’d be a +X weapon and a +Y holy symbol, not necessarily the same value for each. So when you first got it, it would be a +1 weapon, and count as a holy symbol but with no extra frills. Then, “instead” of an uncommon item I might have otherwise given you, I’d have the sword become a +1 holy symbol as well, so at that point it’s +1 for both. I’d then probably alternate between improving the weapon aspects and the holy symbol aspects of the sword.
This is useful because it means I don’t have to worry about “doubling up” on the rewards you get. If both increased together, I might hesitate to give you an increase, where I would if it was just the weapon improving. It also allows me to give different bonuses to the holy symbol, rather than the one offered by wand of the war mage, without basically making it a combination wand of the war mage and whatever other bonuses I put on it.
There are a number of ways to have a holy symbol visible without holding it in your hand.Examples include:
A Holy Symbol Tattoo: Just have it on your forehead or other unarmoured part of your body.
The Cassock of the Clergy. Expensive, but uses the Body slot.
The Create Reliquary Arms and Shields feat. Its a feat, requires crafting, but you can churn out holy symbol weapons and armour.
You can also make your weapon or shield into a Consecrated Weapon or Sanctified Shield, which makes them count as a holy symbol. (Adventurer's Armoury)
I don't see any rules saying that you can't just nail a holy symbol to a shield, but I don't see any rules saying that you can, so it's your DMs call there.
As for amulets, I'm not sure whether you can just... thrust your chest to present the symbol.
Best Answer
Your holy symbol is your spellcasting focus
In addition to being, you know, a symbol of your beliefs and tenets which define your character as a Paladin.
The last subfeature of your Spellcasting feature reads:
Said spellcasting focus can be used to provide non-costed, non-consumed material components for your spells. (See Chapter 10 of the PHB; Spellcasting > Casting a Spell.)
Excatly how it will work being engraved on your sword hilt you'll have to ask you DM about (I personally would expect "yeah, that's fine". The issue is that the two options discussed by the rules are discrete items, or on a shield, but not on a weapon. The relevant rule for the DM:
If that's valid as holding in your hand, or as a simple flavour mod from having it on your shield, it's a no problem spellcasting focus for you.