We　study　phase-controlled　quantum　entanglement　and　one-way　quantum　steering　in　a　cavity　magnonic　system,　where　two　magnon　modes　couple　to　two　microwave　cavities　driven　by　squeezed　fields.　The　magnon-magnon　entanglement　and　the　steering　directivity　can　be　controlled　by　adjusting　the　ratio　of　the　coupling　strengths　between　cavity　modes　and　magnon　modes.　In　particular,　the　quantum　entanglement　and　one-way　quantum　steering　can　be　significantly　enhanced　by　the　squeezed　vacuum　field,　which　also　exhibits　robustness　against　temperature　variations.　More　intriguingly,　both　quantum　entanglement　and　steering　between　two　magnon　modes　are　susceptible　to　variations　in　the　phase　difference　of　two　Josephson　parametric　amplifiers,　and　thus　the　phase-controlled　quantum　entanglement　and　one-way　quantum　steering　can　be　achieved.　Our　scheme　may　have　potential　applications　in　quantum　information.　©　2024　Optica　Publishing　Group　under　the　terms　of　the　Optica　Open　Access　Publishing　Agreement.