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The interactions between the Magellanic Clouds significantly affect the shape and distribution of the young stellar population, particularly in the periphery of the Small Magellanic Cloud (SMC). We present the first far-UV (FUV) map of the north-east SMC-Shell region using the Ultra Violet Imaging Telescope (UVIT) onboard AstroSat. The detected FUV stars are combined with Gaia Early Data Release 3 data to create a FUV–optical catalogue of ∼14 400 stars. FUV–optical colour-magnitude diagrams are used along with isochrones to estimate the stellar ages. The detected stars are formed in multiple episodes. We identified two episodes of star formation (∼60 and ∼260 Myr ago), where the episode at ∼260 Myr is linked to the recent interaction with the Large Magellanic Cloud (LMC) and the episode at ∼60 Myr is linked to the pericentric passage of the SMC around our Galaxy. The median proper motion (PM) and velocity dispersion are found to be similar to the SMC main body, indicating that this region has not experienced significant tidal effects. The FUV stellar surface density and the dispersion in PM suggest that the extent of the inner SMC in the north-east direction to be around 2.2°. We detect arm-like and arc-like structures in the FUV stellar density map, and their kinematics appear to be similar to the SMC main body. These extended outer features are the spatial stellar overdensities formed over multiple episodes of star formation, but without apparent kinematic distinction. [ABSTRACT FROM AUTHOR]