Abstract <p>We obtain exact solutions for electromagnetic field in the Schwarzschild metric. For deriving the field equations a gauge is used, in which the temporal component of the vector potential is identically equal to zero and the gauge condition goes to the Poincaré gauge condition at the horizon and to the Coulomb gauge condition at the infinity. In this gauge, the radial parts of resulting field equations can be reduced to confluent Heun equations and the corresponding solutions can be expressed in terms of confluent Heun functions. They can be obtained also in the form of infinite series by the Frobenius-Thome method. The last representation allows to obtain asymptotic behavior of the radial solutions and evaluate their normalization. The angular part of the obtained solutions is expressed through spherical vectors. Compared to the case of the Minkowski space, a doubling of the number of physically adequate solutions is present.</p>