Do baseband android phone work in Nigeria

Baseband and Quad Band refer to two totally different things. You need a phone that's compatible, not only with the country it's going to be used in, but with the carrier it's going to be used with. Contact the carrier you'll be using in Nigeria and ask what phone specifications THEY need for a phone to work on their system. (For instance, some carriers will not allow you to use a phone they didn't sell you.)