On the equation $m^3-m^2+1 = n^2$

Question

(i) How can I find all positive integers $m$ such that $m\equiv 4 \pmod 7$ and $m^3-m^2+1$ is a perfect square?

(ii) Is there a method to solve this equation over positive integers: $$m^3-m^2+1 = n^2.$$