$7^{103}=7 \times 7^{102}$ 

$\begin{aligned} & =7 \times(49)^{51} \\ & =7 \times(51-2)^{51} \end{aligned}$

Remainder = $7 \times(-2)^{51}$ 

$\begin{aligned} & =-7\left(2^3 \cdot(16)^{12}\right) \\ & =-56(17-1)^{12} \end{aligned}$

Remainder $=-56 \times(-1)^{12}=-56+68=12$