<p>In order to investigate the temporal evolution of the solar magnetic field and different classes of solar flares, and to probe the relationship between them, we study the time-series of the sunspot area and solar flares of M and X class observed on the full solar disk during complete Solar Cycle 24 and the ascending phase of current Solar Cycle 25 i.e., from January 2009 to April 2025, following the new NOAA scaling system. We study periodic and quasi-periodic behavior of the solar indices. It has been established that the solar indices referring to the phenomena occurring at different solar layers exhibit different periodicities, which are confined to various phases of the solar cycle. Our investigation indicates that sunspot area as well as the flare index have higher amplitudes during Cycle 25 than Cycle 24. We noticed that both sunspot area (representing solar magnetic activity) and energetic flares show a number of short and intermediate term periodicities during both Cycle 24 and 25. During Cycle 24 and 25, in the high-frequency range, this covers the solar rotation periods as well as prominent 17 – 60-day periods in the flare data sets. On the other hand, in the intermediate-frequency range, we measured a series of significant quasi-periodicities of 76 – 85, 104 – 120, 147 – 176 days, 183 – 196, 237 – 243, 273 – 295, 328 – 392 days and 1.1 – 1.5 year and ∼ 2.7 year in different phases of Cycle 24 and 25. We have observed that the well-known Rieger-type of periods and Quasi-biennial oscillations of about 1.3 years reappeared during the maximum phase of Cycle 25 in both sunspot area and energetic flare data sets. The cross-correlation and cross-wavelet analysis reveal that both M and X class flares are positively correlated with the sunspot areas with phase mixing (asynchronicity) in both cycles. We discuss our results with the existing numerical models.</p>