I am on a single entry b visa issued in Germany. The visa expires on 12 Jan. Permission to stay on 15 Jan. My question is, can I get an extension of stay,? If yes when and where to get it?

Or should I get a New visa from a neighbouring country?

You can get a one year extension if you have a work permit and supporting documents from an employer. If not you can apply for an extension, pay 1900 baht and be given 7 days to leave the country after it is denied.

Without a work permit or a application approval letter for one you will not be able to get a non-b visa at a nearby location.