Influential community search (ICS) finds a set of densely connected and high-impact vertices from a social network. Although great effort has been devoted to ICS problems, most existing methods do not consider how relevant the influential community found is to specific topics. A few attempts at topic-aware ICS problems cannot capture the stochastic nature of community formation and influence propagation in social networks. To address these issues, we introduce a novel problem of topic-aware most influential community search (TAMICS) to discover a set of vertices such that for a given topic vector q, they induce a $(k, l, η)$-core in an uncertain directed interaction graph and have the highest influence scores under the independent cascade (IC) model. We propose an online algorithm to provide an approximate result for any TAMICS query with bounded errors. Furthermore, we design two index structures and an index-based heuristic algorithm for efficient TAMICS query processing. Finally, we experimentally evaluate the efficacy and efficiency of our proposed approaches on various real-world datasets. The results show that (1) the communities of TAMICS have higher relevance and social influence w.r.t.~the query topics as well as structural cohesiveness than those of several state-of-the-art topic-aware and influential CS methods and (2) the index-based algorithm achieves speed-ups of up to three orders of magnitude over the online algorithm with an affordable overhead for index construction.