When the speed of electron increases, its specific charge

Charge does not change with speed but mass varies with the speed as per relation,

$\mathrm{m} =\frac{ {\mathrm{m}}_{\mathrm{o}}}{\sqrt{1-{\displaystyle \frac{{\mathrm{v}}^2}{{\mathrm{C}}^2}}}}$ 

Hence specific charge e/m decreases with increase in speed.