Can anyone tell me what a yellowish-greenish discharge after my puppy pees is? My vet gave him antibiotics for a UTI but he still has it and he's had it since I got him at 6weeks old he is almost 12weeks and it only appears after he pees?

Could be smegma, a natural lubricant, or it could be effects of the UTI, either way keep giving the antibiotics until they are gone just as directed.

They have been gone for almost a month that's why I'm not sure what to do, do I go back to the vet for him just not to give me much info again?

If it truly is smegma it is nothing to worry about, it is a natural fluid made to keep things lubricated.
Of course I can't see it to tell you if it truly is that or not.
Some make dogs simply don't clean themselves well and you will notice it more so than on a dog who is an immaculate groomer.
He really had a UTI at 8 weeks old? Or were they treating something else?
UTIs are not unheard of at such a young age, just doesn't happen that often.
Were they treating the discharge that you are seeing now? Did they do a urinalysis?

Yes they treated him for it but didn't look or take any samples just asked me what was wrong then picked out a medicine and gave to him

Ok, now I'm confused.
Are you saying that you had the pup at the vet, and not only did they not look at the discharge that is worrying you, but they didn't properly check for an UTI and just gave you some antibiotics to give him?
IF that is true, that is just poor medicine and I would be finding myself a different vet.
If I am wrong in thinking that, please, please correct me.