That doesn't exist in 5e.
In general, if you need to touch the target, this is handled as part of casting the spell, with a melee spell attack to determine if you succeed. For example, shocking grasp:
Lightning springs from your hand to deliver a shock to a creature you try to touch. Make a melee spell attack against the target. You have advantage on the attack roll if the target is wearing armor made of metal. On a hit, the target takes 1d8 lightning damage, and it can't take reactions until the start of its next turn.
If the spell attack fails, the spell does nothing. Note, since you're used to the mechanics from 3rd edition, that spell attacks are rolled against the target's normal AC.
There are a few exceptional cases:
Spells that act like weapons
This includes flame blade and vampiric touch. These also use melee spell attacks, but the spell lasts for some duration and allows you to make additional attacks during that time.
Spells that boost weapon attacks
The various paladin "smite" spells such as branding smite are all verbal-only bonus action spells (so you can cast them with a weapon in hand and immediately attack) with a duration of 1 minute. Once the spell is cast, the next time you hit someone with a melee weapon, the spell adds damage and other effects. This is arguably the most similar to the "held touch spell" from 3rd edition: you make your attack, and if you miss, it carries over to your next attack. However, they're not "touch" spells; you're still making normal weapon attacks.