Secondary ice production (SIP) leads to the formation of new ice particles from preexisting ones. Besides generating ice crystals, SIP can also influence cloud characteristics, including convection, precipitation, and even radiative properties. This study examines the effect of ice crystal formation by Hallett-Mossop, fragmentation of freezing drops, and fragmentation due to ice-ice collision processes in an idealized deep convective cloud observed during the HAIC/HIWC campaign, using the 3D bin microphysics scheme DESCAM. Our results indicate that heterogeneous ice nucleation and fragmentation of freezing drops play a role during the early formation of the cloud while after that, Hallett-Mossop and ice-ice breakup processes dominate, representing 17.6% and 81.5% of the ice crystal production, for temperatures warmer than -30°C. For temperatures colder than -30°C, homogeneous and heterogeneous ice nucleation processes are the main contributors to ice crystal formation. The impact of each SIP process on particle size distributions is analyzed by tracking air parcel trajectories. This study also shows the effect of SIP processes on cloud development. Implementing SIP results in a decrease in cloud top altitude by around 1.5 km. Our analysis shows that this effect is caused by increased latent heat released below 11 km, resulting from a stronger vapor deposition on more numerous ice crystals. This enhances convection at lower levels but inhibits it above. Furthermore, incorporating SIP leads to 15% decrease in total precipitation amount and 25% reduction of intense rainfall (accumulated precipitation over 40 mm). Hence, our study emphasizes the importance of SIP mechanisms in cloud development and precipitation.