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The fermionic and bosonic zero modes of the 1D interacting Kitaev chain atthe symmetric point are unveiled. The many-body structures of the Majorana zeromodes in the topological region are given explicitly by carrying outperturbation expansion up to infinite order. We also give the analyticexpressions of the bosonic zero modes in the topologically trivial phase. Ourresults are generalized to the hybrid fermion system comprised of theinteracting Kitaev model and the Su-Schrieffer-Heeger model, in which we showthat these two types of zero modes can coexist in certain region of its phasediagram.

Explicit forms of zero modes in symmetric interacting Kitaev chain without and with dimerization