Backgrounds don't grant that kind of feature
Backgrounds grant two proficiencies (generally two skills and two of languages, tools, instruments, etc.) and a story/worldinteraction type feature, not something like a damage resistance.
The feat Infernal Constitution (Xanathar's page 75) grants you resistance against poison damage (and advantage on saves against being poisoned). It does, however, require you to be a tiefling who don't get bonuses to wisdom.
All dwarves (PHB pages 18-20) get resistance to poison and hill dwarves get a bonus to their wisdom.
Aasimar (Volo's pages 104-105) get resistance to necrotic damage and protector assimars get a bonus to wisdom.
Dragonborn (PHB pages 32-33) get resistance to one damage type which for green ones is poison damage. They do however not get bonuses to their wisdom.
Warforged (E:RftLW page 36) from Eberron get resistance to poison damage and advantage on saves against poison, and can choose to get a bonus to wisdom. Ask your DM whether Eberron content is right for you.
Yuan-Ti (Volo's page 120) get immunity to poison damage, but no bonus to their wisdom and as a monstrous adventurer you will especially need to talk with your DM about availability and what place the race has in that world.
Low level spells
In part mentioned because it is not available to magic initiate as protection from poison is a 2nd level spell. It is however a spell on the cleric list which grants resistance to poison damage and advantage on saves against the poisoned condition, in addition to neutralising an extant poisons.