For \(\alpha \in [0,1)\) , let \(A_{\alpha }(G)=\alpha D(G)+(1-\alpha )A(G)\) , where D(G) and A(G) are the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. The \(A_{\alpha }\) -spectral radius of G is equal to the largest eigenvalue of \(A_{\alpha }(G)\) . In this paper, we explore some sufficient conditions for the existence of a \(\{P_{2}, C_{3}, P_{5}, \mathcal {T}(3)\}\) -factor in a graph. We first provide a tight edge number condition to ensure the existence of \(\{P_{2}, C_{3}, P_{5}, \mathcal {T}(3)\}\) -factors in the graph. Moreover, we derive a tight sufficient condition, expressed in terms of the \(A_{\alpha }\) -spectral radius, for the existence of \(\{P_{2}, C_{3}, P_{5}, \mathcal {T}(3)\}\) -factors in graphs, which generalizes the result of Zhou (2025) for \(\alpha =0\) .
