Time　periodic　driving　can　serve　as　synthetic　gauge　fields　and　plays　a　key　role　in　simulating　dynamical　topological　materials.　The　periodically　driven　systems,　where　different　spins　(or　sublattices)　are　engaged　in　the　different　dynamical　driving　processes　are　investigated.　It　is　demonstrated　that　spin-dependent　time-periodical　periodic　driving　can　result　in　shifted　topological　edge　modes　with　non-zero　(nor　+/-　omega/2)　quasi-energies.　Such　shifted　topological　edge　modes　are　not　only　related　to　the　spin　imbalance　at　each　instantaneous　time,　but　also　the　details　of　the　dynamical　driving.　Here,　it　is　also　illustrated　that　the　spin-dependent　time-periodical　driving　can　be　conceived　as　the　time-spin　coupling,　and　similar　to　the　static　spatial　spin-orbit　coupling,　tuning　time-spin　coupling　parameters　can　lead　to　topological　phase　transitions.　Experimental　simulations　on　the　spin-dependent　time-periodic　driving　are　proposed　by　shaking　optical　super-lattices　and　Raman　assisted　tunneling.