In this talk, we discuss a variant of the Conley conjecture which asserts the existence of infinitely many periodic orbits of a symplectomorphism if it has a fixed point which is unnecessary in some sense. More specifically, we discuss a result claiming that, for a certain class of closed monotone symplectic manifolds, any symplectomorphism isotopic to the identity with a hyperbolic fixed point must necessarily have infinitely many periodic orbits as long as the symplectomorphism satisfies some constraints on the flux.