What is the nerve involved in this condition?

Obturator- With scissor gait there is overactive adduction of the thigh. So, you need to identify which nerve innervates the adductor compartment. And that nerve is the obturator nerve. The obturator nerve innervates the medial compartment of the thigh, including adductor longus, magnus, and brevis. If the obturator nerve was firing too much, the leg would be constantly adducting, causing the scissor gait. The femoral nerve innervates the quadriceps muscles, which extend the leg at the knee.

The inferior gluteal nerve innervates gluteus maximus, which is important for powerful extension of the thigh. The tibial nerve innervates the hamstrings, which flex the knee and extend the thigh. The tibial nerve also innervates the muscles of the posterior compartment of the leg, which plantarflex the foot.