The series is most likely Prodigal Son. It follows Malcolm Bright, who is forced to reconnect with his imprisoned father, Martin Whitly, a serial killer.

Why this fits

  • The main character is linked to a father who is in prison.
  • The story centers on their confrontation and repeated meetings outside the prison setting.
  • It is a TV drama, not a film.

Other possibility

  • Starred Up is a film, not a TV series, but it also features a son meeting his father in prison.

TL;DR: If you mean a TV series, the answer is probably Prodigal Son.