In this work systems of sines $\sin \left(n+\beta \right)t,\, \, n=1,2, \ldots,$ and cosines $\cos \left(n-\beta \right)t,\, \, n=0,1,2, \ldots,$ are considered, where $\beta \in R-$is a real parameter. The subspace $M^{p,\alpha } \left(0,\pi \right)$ of the Morrey space $L^{p,\alpha } \left(0,\pi \right)$ in which continuous functions are dense is considered. Criterion for the completeness, MINIMALITY and basicity of these systems with respect to the parameter $\beta $ in the subspace $M^{p,\alpha } \left(0,\pi \right)$, $1