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Helical edge states in topological insulators generate a counterpropagating spin current on the two parallel edges. We here propose antihelical edge states of magnons in patterned antiferromagnetic thin films, which host a copropagating spin current on the two parallel edges, where the two magnon modes with opposite chirality act like the spin. The embedded heavy metal dot array in the thin film induces interfacial Dzyaloshinskii-Moriya interactions (iDMIs), drives the magnon bands into nontrivial topological phases, characterized by spin Chern number. The resulting helical edge modes lead to spin current with the direction dependent on the sign of the iDMI parameter. In a strip geometry, we combine two subsystems with two embedded metal dot arrays, which give opposite iDMI parameters. Antihelical edge states emerge, compensated by the counterpropagating bulk-confined states. Helical and antihelical edge states are verified by the micromagnetic simulations. We consider these results promising and inspiring for further developments of magnon spintronic devices based on antiferromagnets.