I am playing as the evil half-elf bard from the premade character selection. Recently I just noticed in the character sheet that my strength is suffereing a debuff. I am uncertain what has caused this? Resting does not get rid of it. What caused this and how can I remove it?

You should state which game of the series you are talking of.

Anyway some kind of ability debuffs are permanent and can't be cured by resting: to cure the ability drain you need to use a "Restoration" spell.
Just look for a temple and search for a cleric who offers healing services: they are surely able to cure you.

Neverwinter Nights Diamond

There are lots of possible sources. Where are you in the game? What have you been doing recently? How long has it been since you noticed the debuff?

I have been doing the beggers nest but needed to go back and upgrade equipment etc. I discovered that after using the stone that returns you to the temple. The main quest giver Aribeth heals those annoying debuffs. I found out one way to remove them by luck.

I seem to recall that most acts have a healer that will restore you to full hp and remove bad statuses when asked.

I don't remember what could cause strength damage/drain in the beggar's nest. Might have been a negative energy trap? Attacks by Shadows do strength damage, but it comes back after time passes (I don't remember if just resting is sufficient). I think disease might cause stat damage, but resting should eventually let you make enough Fort saves to take care of it. Any strength drain spells should have worn off after a while.

Could be the spider poison. That stuff drains strength and is quite long lasting if not permanent.

This is correct. Those spiders are annoying if you don't have antidote potions or restoration spells. If you don't, It requires using the stone to return to Aribeth and paying the man 50g to warp you back where you were again.