We present the photometric and spectroscopic studies of a Type Ib SN 2015ap and a Type Ic SN 2016P. SN 2015ap is one of the bright (M_V = −18.04 mag) Type Ib while SN 2016P lies at an average value among the Type Ic SNe (M_V = −17.53 mag). Bolometric light-curve modelling of SNe 2015ap and 2016P indicates that both the SNe are powered by ⁵⁶Ni + magnetar model with ⁵⁶Ni masses of 0.01 and 0.002 M_⊙, ejecta masses of 3.75 and 4.66 M_⊙, spin period P₀ of 25.8 and 36.5 ms, and magnetic field B_p of 28.39 × 10¹⁴ and 35.3 × 10¹⁴ G, respectively. The early spectra of SN 2015ap show prominent lines of He with a ‘W’ feature due to Fe complexes while other lines of Mg ii, Na i, and Si ii are present in both SNe 2015ap and 2016P. Nebular phase [O i] profile indicates an asymmetric profile in SN 2015ap. The [O i]/[Ca ii] ratio and nebular spectral modelling of SN 2015ap hint towards a progenitor mass between 12 and 20 M_⊙.