PURPOSE: LATTICE, a form of spatially fractionated radiation therapy that delivers high-dose peaks and low-dose valleys within the target, has been clinically utilized for treating bulky tumors. However, its application to small-to-medium-sized target remains challenging due to beam size limitations. To address this challenge, this work proposes a novel proton LATTICE (pLATTICE) modality using minibeams, namely minibeam-pLATTICE, that extends LATTICE approach for small-to-medium targets. METHODS: Three minibeam-pLATTICE methods are introduced. (1) M0: a fixed minibeam orientation for all beam angles
(2) M1: alternated minibeam orientations, for consecutive beam angles
(3) M2: multiple minibeam orientations for each beam angle. For each minibeam-pLATTICE method, an optimization problem is formulated to optimize dose uniformity in target peaks and valleys, as well as dose-volume-histogram-based objectives. This problem is solved using iterative convex relaxation and alternating direction method of multipliers. RESULTS: Three minibeam-pLATTICE methods are validated to demonstrate the feasibility of minibeam-pLATTICE for head-and-neck cases. The advantages of this modality over conventional beam (CONV) pLATTICE are evaluated by comparing peak-to-valley dose ratio (PVDR) and dose delivered to organs at risk (OAR). All three minibeam-pLATTICE modalities achieved improved plan quality compared to CONV, with M2 yielding the best results. For example, in terms of PVDR, M2=5.89, compared to CONV=4.13, M0=4.87 and M1=4.7. CONCLUSION: A novel minibeam-pLATTICE modality is proposed that generates lattice dose patterns for small-to-medium targets, which are not achievable with conventional pLATTICE due to beam size limitations.