We demonstrate and study a microcell microwave atomic clock based on optical-microwave Double Resonance (DR) interrogation operated in pulsed Ramsey scheme, called the POP clock, based on a micro-fabricated Rb vapor cell and a micro-loop-gap microwave resonator. For the mm-scale dimensions of this cell, the population and coherence relaxation rates of the Rb clock transition are on the order of 45 kHz, which puts constraints on the useful Ramsey times and overall pulse sequence in view of optimized clock performance. Our proof-of-principle demonstration of the POP clock shows that pulsed DR approach is nevertheless feasible and results in a short-term clock stability of 1×10-11 -1/2 and reaching the ≤ 2×10-12 level at timescales of 1 000 s to one day. The short-term instability budget established for the POP clock shows that the main limitation to the short-term stability arises from the detection noise. Thanks to the pulsed Ramsey scheme, light-shift effects are strongly reduced in the POP clock which opens perspectives for further improvements of long-term clock stability, in view of new generations of miniature vapor-cell clocks with enhanced performances based on the DR scheme.