If you are in the area of Hat Yai then you can find Thai Immigration in Hat Yai at the details listed below. Note they cannot issue you a Thai visa and can only extend your visa. You need to cross the border into Malaysia and apply for a visa at the Thai embassy in KL or the Thai embassy in Penang.
You can however do your 90 day reporting with them and you can apply for a re-entry permit if you have a 12 month visa and will be crossing the Thai border and wanting to return with your visa status as it is now. Note that they can extend your tourist visa, retirement visa or marriage visa while in Hat Yai.
Thai Immigration in Hat Yai
99 Moo 3
Amphoe Khlong Hoi Khong