We search, for the first time, for an exotic molecular state with quantum numbers JPC = 1(-+), called X, via the process e(+)e(-) -> gamma D-s(+) D-s1(-) (2536) + c.c. using data samples corresponding to a luminosity of 5.8 fb(-1) across center-of-mass energies from 4.612 to 4.951 GeV, collected with the BESIII detector operating at the BEPCII Collider. No statistically significant signal is observed. The upper limits on the product of cross section and branching fraction sigma(e(+)e(-) -> gamma X) . B(X -> D-s(+) D-s1(-) (2536) + c.c.) at 90% confidence level are reported for each energy point, assuming the X mass to be 4.503 GeV/c(2) and the width 25, 50, 75, and 100 MeV, respectively.