In this paper, we first study the Laplace equation in AdS2 space with electromagnetic field. In order to construct the corresponding Schr¨odinger equation, we write the metric and vector potential in suitable way. So, in that case, we face with Schr¨odinger equation in AdS2 space. By using factorization method, we factorized the second order equation in terms of first order equations. These first order operators show that our system has a some shape invariance condition. It leads us to obtain the supercharges and corresponding commutative relation. Finally, we show that these supercharges will be form of generators of algebra
