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We present a detailed view of cluster formation (CF) to trace the evolutionand interaction history of the Magellanic Clouds (MCs) in the last 3.5 Gyr.Using the \textit{Gaia} DR3 data, we parameterized 1710 and 280 star clustersin the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC), where847 and 113 clusters are newly characterized in the outer LMC and SMC,respectively. We estimated the age-extinction-metallicity-distance parametersusing an automated fitting of the color-magnitude diagram (CMD) after fieldstar removal, followed by an MCMC technique. We report a first-time detectionof two synchronized CF peaks in the MCs at 1.5$\pm$0.12 Gyr and 800$\pm$60 Myr.We recommend that the choice of the metallicity ($Z$) values of isochrones forclusters with age $\le$ 1 - 2 Gyr are Z$_{\text{LMC}}$ = 0.004 - 0.008 andZ$_{\text{SMC}}$ = 0.0016 - 0.004 for the LMC and SMC, respectively. We foundevidence for spiral arms in the LMC, as traced by the cluster count profilesover the last 3.5 Gyr. The density maps provide evidence of ram-pressurestripping in the North-East of the LMC, a severe truncation of CF in the Southof the LMC, and a radial shrinkage of CF in the SMC in the last 450 Myr. Thelast SMC-LMC interaction ($\sim$ 150 Myr) resulted in a substantial CF in theNorth and Eastern SMC, with a marginal impact on the LMC. This study providesimportant insights into the CF episodes in the MCs and their connection to theLMC-SMC-MW interactions.

Spatio-temporal map of star clusters in the Magellanic Clouds using Gaia: Synchronized peaks and radial shrinkage of cluster formation