We　study　the　dynamic　generation　of　persistent　current　by　phase　imprinting　fermionic　atoms　in　a　ring　geometry　at　zero　temperature.　Mediated　by　the　pairing　interaction,　the　Fermi　condensate　dynamically　acquires　a　quantized　current　by　developing　azimuthal　phase　slips,　as　well　as　density　and　pairing-order-parameter　depletions.　Resorting　to　the　Bogolioubov-de　Gennes　formalism,　we　investigate　the　time　evolution　of　the　transferred　total　angular　momentum　and　the　quantized　superfluid　current　throughout　the　phase-imprinting　process.　This　enables　a　detailed　self-consistent　analysis　of　the　impact　of　interaction,　as　well　as　different　initial　pairing　states,　on　the　superflow　formation,　in　contrast　to　previous　theoretical　analysis　based　on　the　Gross-Pitaevskii　equation　with　artificially　imposed　phases.　In　particular,　we　show　that,　as　the　interaction　strength　increases,　the　azimuthal　density　distribution　becomes　less　susceptible　to　the　phase　imprinting　potential,　leading　to　a　smaller　quantized　current　under　the　same　imprinting　parameters.　Our　results　offer　microscopic　insights　into　the　dynamic　development　of　superflow　in　the　phase-imprinting　process,　and　are　helpful　for　the　ongoing　experimental　effort.