This reminds me of the golden rule, as in, he who has the gold makes the rules.
When I used to write leases in another life, there was a typical clause that I would include that says that the tenants shall not have a guest (ie, not someone on the lease) over for sustained periods of time, usually more than 10 days in a 30 day period. This clause may or may not be there and even if it is, your boyfriend's father may not be able to enforce that provision. But, he is the one paying the bills.
What would your boyfriend do if he suddenly stopped? He'd be kicked out with you.
In such a circumstance, it would have been best to have a written agreement among you, the Dad and your boyfirend about how the expenses will be handled. If you had a written agreement about paying the bills, then the written agreement would govern and could not be changed except by another written agreement that you, the Dad and your boyfirend all sign.
I am going to assume that there is no written agreement, since you did not mention one. In that case, none of the tenants (you, Dad or boyfriend) has the legal right to make any other tenant leave the apartment. However, if the Dad stops paying the rent, the Landlord will be able to evict you, your boyfirend and you Dad and sue any one of you for the entire amount of rent. It is most likely that the Landlord will choose to sue you all, but will be able to collect only from the Dad, whom I assume has the money. The Dad then may not want to stop paying the rent because of the liability he'll have.
Practically speaking, the Dad is going to make living at the apartment very unpleasant for you and your boyfriend. And your options are to move out without your boyfriend, move out with your boyfriend, or stay there and do what the Dad says.