The first results on the σLT′ structure function in exclusive π0p electroproduction at invariant masses of the final state of 1.5GeV \u3c W \u3c 1.8 GeV and in the range of photon virtualities 0.4 GeV2 \u3c Q2 \u3c 1.0 GeV2 were obtained from data on beam spin asymmetries and differential cross sections measured with the CLAS detector at Jefferson Lab. The Legendre moments determined from the σLT′ structure function have demonstrated sensitivity to the contributions from the nucleon resonances in the second and third resonance regions. These new data on the beam spin asymmetries in π0p electroproduction extend the opportunities for the extraction of the nucleon resonance electro-excitation amplitudes in the mass range above 1.6 GeV