Krusty the Clown is one of the most enduring characters in The Simpsons. He first appeared in the 35th The Simpsons short, "The Krusty the Clown Show," which originally aired on The Tracey Ullman Show in January, 1989. Krusty's father, on the other hand, isn't nearly as well known as his son, and this could partially be because he was killed of in Season 26.
Rabbi Hyman Krustofsky's first appearance was in Season 3, Episode 6, "Like Father, Like Clown," when it is revealed that a young Krusty had performed at a Rabbi convention, but he was sprayed with seltzer, resulting in his clown makeup rubbing off. His father recognizes him and disowns Krusty out of shame. Being a respected Rabbi from a long legacy of Rabbi ancestors, he also expected his son to follow suit. Despite their past, this episode comes to a climax with the pair reconciling in the then-present day, with Rabbi Krustofsky accepting that entertainers have a place in Jewish heritage; however, their relationship ends in tragedy years later.
In Season 26, Episode 1, "Clown in the Dumps," Krusty is brutally roasted by fellow comedian Sarah Silverman. Hurt and offended by Silverman's words, he seeks comfort from his father, but when he asks him if he genuinely finds him funny, Rabbi Krustofsky replies, "if you want to know my honest opinion of you, you've always been... eh." He then passes away before getting the final word.
This unclear answer to Krusty's question would be at least somewhat clarified later in the episode, when he discovers that his father's favorite comedian told the same jokes that he would tell on stage himself. Based on this, it's highly likely that his father did find him funny, but this doesn't change the fact that their relationship during his life was strained.
Rabbi Krustofsky actively sought to prevent his son from becoming a clown, and this notion is enhanced when he finds out his son had received his first laugh by mocking him on stage. When he inadvertently sees him performing with his own eyes at the aforementioned Rabbi convention, the pair became completely estranged for many years.
It is actually Krusty's biggest fans, Bart and Lisa Simpson, who help to bring the two back together. Their mission involves quoting passages of Jewish scripture, but after that fails, Bart finally succeeds in convincing Rabbi Krustofsky to reconcile with his son by quoting Sammy Davis Jr. He would go on to meet his son backstage on The Krusty the Clown Show, and the two embrace after years apart. Rabbi Krustofsky even appears in front of the show's audience, playfully throwing a pie at Krusty.
All that being said, Krusty and his dad have actually been on screen together a number of times in The Simpsons - perhaps most notably in Season 15, Episode 6, "Today, I Am a Clown." In the episode, Krusty comes to the realization that his lack of a Bar Mitzvah is preventing him from finding happiness, so he reunites with his father once more in order to make it happen. Rabbi Krustofsky goes on to teach Krusty all about Judaism, and his Bar Mitzvah goes ahead with the two sharing a rare moment of happiness together.