The phenomenon of paternally dependent familial twinning has been known in human and animal genetics since the 1920s, but still remains without any theoretical explanation and is indeed a neglected field of inquiry. Over the last two decades investigations in reproduction biology have discovered the significant role of multiple paternally dependent errors in fertilization including androgenic triploidy and moles. We suggest the hypothesis that the fathers of twins in the relevant families carry gene variants that increase the probability of dispermy, diplospermy and male pronucleus heterochrony as well as involvement of two male pronuclei in the fertilization of two female meiotic products. Any resulting twins would be an exceptional intermediate between MZ and DZ twins — and might properly be described as “sesquizygotic” (SZ). Paternal familial twinning may also go together with infertility due to triploidy, moles and chimerism. The hypothesis: (i) places the curiosities of paternally derived twinning within the framework of current knowledge of reproductive genetics and verifiable phenomena; (ii) predicts the existence of families in which twinning is associated with reproductive abnormalities; (iii) predicts an occurrence in relevant families of the third and intermediate category of SZ twins. Families with paternal twinning may thus provide the natural selective system for the search of unusual cases of primary chimeras, the frequency of which is still unknown.