We investigate the emergence of synchronization blockade arising from the combined action of external driving and internal exchange interactions in quantum oscillators. The external drive indirectly influences the undriven mode through coupling to the driven mode, leading to a breakdown of limit cycle behavior in the Wigner function. Concurrently, the interplay of driving and coupling transforms dressed-state peaks into a Mollow-like triplet in the power spectrum. An asymmetric synchronization blockade is revealed in the phase measures, where the undriven mode remains phase locked to the drive even when the driven mode is at blockade. Using the relative entropy of coherence, we establish that resonant blockade is associated with the suppression of coherence due to the competing effects of drive-induced coherence and its redistribution via exchange interactions.

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• Synchronization
• Collective dynamics
• Phase space methods