Finite groups with some weakly $S\mathrm{\Phi }$-supplemented subgroups

Let $G$ be a finite group. A subgroup $H$ of $G$ is called $s$-permutable in $G$ if $H$ permutes with every Sylow subgroup of $G.$ A subgroup $H$ of $G$ is called weakly $S\mathrm{\Phi }$-supplemented in $G$ if there exists a subgroup $K$ of $G$ such that $G=HK$ and $H\cap K\le \mathrm{\Phi }(H)H_{sG},$ where $\mathrm{\Phi }(H)$ is the Frattini subgroup of H and $H_{sG}$ is the subgroup of $H$ generated by all these subgroups of $H$ that are $s$-permutable in $G.$ Using this concept, some results for a group to be $p$-nilpotent and supersolvable are given. These results improve and extend some new and recent results in the literature.