How does the body produce B and T lymphocytes with specific recognition for antigens?

The body produces antibodies that have both an Fc region (constant) and a variable region (as a result of gene splicing). In this manner, the body produces the millions of variant antibodies (called polyclonal) that circulate through the body's vessels. When one of those unique antibodies finds its antigenic match via the MHC molecule on the surface of an antigen presenting cell, this signals the b cell to pump out antibodies of the same configuration (monoclonal antibodies) to then proceed to remove the invader.