The pathogenesis of ocular adnexal marginal zone lymphomas of mucosa-associated lymphatic tissue-type (OAML) is not fully understood. We performed whole genome sequencing (WGS) and/or whole exome sequencing (WES) for 13 cases of OAML and sequenced 38 genes selected from this analysis in a large cohort of 82 OAML. Besides confirmation of frequent mutations in the genes transducin beta like 1 X-linked receptor 1 (TBL1XR1) and cAMP response element binding protein (CREBBP), we newly identifed JAK3 as a frequently mutated gene in OAML (11% of cases). In our retrospective cohort, JAK3 mutant cases had a shorter progression-free survival compared with unmutated cases. Other newly identified genes recurrently mutated in 5–10% of cases included members of the collagen family (collagen type XII alpha 1/2 (COL12A1, COL1A2)) and DOCK8. Evaluation of the WGS data of six OAML did not reveal translocations or a current infection of the lymphoma cells by viruses. Evaluation of the WGS data for copy number aberrations confirmed frequent loss of TNFAIP3, and revealed recurrent gains of the NOTCH target HES4, and of members of the CEBP transcription factor family. Overall, we identified several novel genes recurrently affected by point mutations or copy number alterations, but our study also indicated that the landscape of frequently (>10% of cases) mutated protein-coding genes in OAML is now largely known.