'Subsequent' is Latin for 'following close behind' — from 'sub-' + 'sequi' (to follow).
Coming after something in time; following.
From Latin 'subsequēns,' present participle of 'subsequī' (to follow closely, to come after, to succeed), from 'sub-' (under, close to, near, from below) + 'sequī' (to follow, to pursue), from PIE *sekʷ- (to follow, to perceive). The 'sub-' prefix here means 'close behind' rather than 'under' — the subsequent thing follows closely on the heels of what came before. PIE *sekʷ- is remarkably productive: Latin 'sequī' gave English 'sequence
The prefix 'sub-' in 'subsequent' does not mean 'under' in the spatial sense but rather 'close behind' — the same use found in 'succeed' (Latin 'sub-' + 'cēdere,' to go close behind, hence to follow). In many Latin compounds, 'sub-' carries this sense of close proximity or immediate succession rather than its more familiar 'underneath' meaning.