Biden bragged about getting a prosecutor (Viktor Shokin) fired, by threatening to withhold aid to Ukraine. A video and transcript are available here:
I remember going over and convincing our team, others, to convince that we should be providing for loan guarantees. And I went over, I guess, the 12th, 13th time to Kiev. And I was supposed to announce that there was another billion-dollar loan guarantee. And I had gotten a commitment from Poroshenko and from Yatsenyuk that they would take action against the state prosecutor. And they didn’t.
So they said they had—they were walking out to a press conference. I said, nah, I’m not going to—or, we’re not going to give you the billion dollars. They said, you have no authority. You’re not the president. The president said—I said, call him. (Laughter.) I said, I’m telling you, you’re not getting the billion dollars. I said, you’re not getting the billion. I’m going to be leaving here in, I think it was about six hours. I looked at them and said: I’m leaving in six hours. If the prosecutor is not fired, you’re not getting the money. Well, son of a bitch. (Laughter.) He got fired. And they put in place someone who was solid at the time.
Biden did not say that the prosecutor was investigating or prosecuting Biden's son.
However, according to an April 2019 article the prosecutor Shokin is quoted as saying that before being fired he had specific plans for:
interrogations and other crime-investigation procedures into all members of the executive board, including Hunter Biden
See also this May interview of Viktor Shokin. According to a google-translation:
[question] That is, the Americans imposed Sakvarelidze on you? And he was a conductor of their interests?
[answer] Partly so, but not of America’s interests, but of Biden’s personal interests (I share this clearly). Specifically, it was Biden who stood behind all this. Then Biden landed here "landing" of such managers who are personally indebted to him and are on his content and contentment. Everyone knew about it.
In other words, David Sakvarelidze was installed as deputy prosecutor in February 2015, and Shokin is saying that Sakvarelidze served Biden's personal interests. This is about 1 year prior to Shokin being forced out by Biden.
The interview continues:
[Question] That is, in the "Burisma case" the prosecutors were not going to "turn on the back"?
[Answer] “No, we were going to interrogate Biden Jr., Archer, and so on.”
Overall, yes Biden bragged about threatening to withhold aid in order to get a prosecutor fired, but there is no proof that Biden's son was the reason for this coercion. Shokin says that Biden acted based upon Biden's personal interests, but others insist that Biden acted out of general EU, US, and/or IMF interests.