We present a rigorous justification for the applicability of the recently developed methods of generalized autobalanced Ramsey spectroscopy (GABRS) [V. I. Yudin, Phys. Rev. Appl. 9, 054034 (2018)2331-701910.1103/PhysRevApplied.9.054034] and combined error signal in Ramsey spectroscopy (CESRS) [V. I. Yudin, New J. Phys. 20, 123016 (2018)NJOPFM1367-263010.1088/1367-2630/aaf47c] for resonances of coherent population trapping (CPT). A protocol of modified combined error signal for CPT resonances is also proposed, in which two successive interrogations of atoms under different times of free evolution are integrated in one cycle. The implementation of the GABRS and CESRS methods in a compact atomic clock based on the CPT effect allows us to significantly suppress the light shift and its fluctuation, which will lead to an improvement in the long-term stability and accuracy of these devices. Moreover, these spectroscopic schemes are insensitive to various distortions of the pulse shape, relaxation processes, errors in the generation of phase jumps, etc., which provides their high reliability and immunity to perturbations.