Periodic behaviors of solar magnetic indicators might provide a clue for the understanding of solar dynamic processes. Combining with a Lomb–Scargle periodogram, the concentration of frequency and time via a multitapered synchrosqueezed transform is applied to investigate the periodic variations of modified coronal index for the time interval from 1 January 1939 to 31 August 2020. The main results are as follows: (1) During solar cycles 19 to 23, the Schwabe cycle of the modified coronal index is operating with its length variating between 10.5 and 11-yr, and the average value of length is 10.67-yr with standard deviation of 0.14-yr. (2) The Rieger-type periods are mainly distributed in a range from 120 to 200 days. In addition, the periods vary somewhat intermittently during cycles 18 to 24, which are operating with the highest power in cycles 21 and 22 while the power is much lower in cycles 23 and 24. (3) For rotation periods, the temporal variation exhibits a highly intermittent pattern as an asymmetrical distribution with its 25th, 50th, and 75th quantile of 26, 27.8, and 31-day, respectively. (4) Other mid-range periods are also detected with an average period length of 8.07, 5.44, 3.42, 2.3, and 1.01-yr.