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A submanifold $M^m$ of a generalized Sasakian-space-form ${\overline{M}}^{2n+1}(f_1,f_2,f_3)$ is said to be $C$-totally real submanifold if $\xi \in \Gamma \left(T^{\perp }M\right)$ and $\phi X\in \Gamma \left(T^{\perp }M\right)$ for all $X\in \Gamma \left(TM\right)$. In particular, if $m=n$, then $M^n$ is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.