We　study　the　shot　noise　of　a　strongly　correlated　quantum　dot　system　in　the　Kondo　regime,　concentrating　on　the　joint　effect　of　a　magnetic　field　B　and　intralead　Coulomb　interaction.　A　shot　noise　formula　is　derived.　The　shot　noise　is　suppressed　by　the　magnetic　field　when　the　intralead　interaction　is　weak,　but　improved　by　the　field　when　the　interaction　is　strong.　The　differential　shot　noise　has　a　peak　or　valley　at　eV　=　+/-　g　mu　B-B　for　weak　or　moderately　strong　intralead　interaction.　As　the　interactions　increase,　these　singular　behaviours　gradually　disappear.　In　the　strong　interaction　limit,　the　shot　noise＇s　curve　has　a　power-law　dependence　on　the　voltage.　The　intralead　Coulomb　interaction　also　modulates　the　Fano　line　shape　of　shot　noise.　The　Fano　factor　is　enhanced　by　the　magnetic　field　and　dot-lead　asymmetric　coupling　and　is　always　sub-Poissonian　noise.