Maceo Parker is well known as the sax player that played on many of James Brown's most famous tracks ("Take it Maceo"). However he has created an admirable body of work with his own groups. My favorite album of his is Southern Exposure. Blues for Shorty Bill is the first track and gives a good representation of the funky grooves Maceo is known for. There is a nice very down home vocal and groove on Every Saturday Night. He applies a New Orleans approach to Mercy, Mercy, Mercy to great effect. His soloing can create really interesting rhythmic developments with the use of just 3 or 4 notes. He can also blow long jazzy phrases as you can hear in the stunning arrangement (with parallel soloing) of the jazz standard The Way You Look Tonight. The last link on this page will give you access to the entire album. A really nice mix of jazzy blues and funky grooves awaits you.
https://www.youtube.com/playlist?list=OLAK5uy_n8QDObEAgxpf326jc-hsG2qctzPCmmUzA