The perspectives of genomic citizen scientists on ownership of research outputs are not well understood, yet they are useful for identifying alignment of participant expectations and project practices and can help guide efforts to develop innovative tools and strategies for managing ownership claims. Here, we report findings from 52 interviews conducted in 2018 and 2019 to understand genomic citizen science stakeholders' conceptualizations of, experiences with, and preferences for ownership of research outputs. Interviewees identified four approaches for recognizing genomic citizen scientists' ownership and related credit interests in research outputs: shared governance via commons models; fractional ownership of benefits; full and creative attribution; and offensive and defensive patenting. Interviewees also agreed that the model selected by any project should at least maximize access to research outputs and, as appropriate and to the extent possible, broadly distribute rights of control and entitlements to research benefits.