Inheritance of traits related to yield and fatty acid profile of winter squash seed oil

•Additive effects were predominant for most traits assessed in the present study.•Overdominance was found for oil content (OL%).•Conducting progeny tests over the generations of selfing for traits that expressed significant dominance effects will enable the distinction between genotypes, thus enabling greater efficiency in selection and providing greater genetic gains.•Recurrent intrapopulation selection in early generations for most of the characteristics studied may be useful to increase the frequency of favorable alleles for the development of an open-pollinated variety with higher oil productivity associated with greater stability of the functional oil.•In general, the high magnitudes of genetic correlations were observed, which are favorable for the increase in oil productivity and improvement of the fatty acid profile in pumpkin.