I don't plan to quibble with you about what a "study" is or go to effort to spoon-feed you with information you could easily get for yourself if you wanted to know about it. That said, here's an excerpt from the first website I came across:
"Michael E. Lamb is head of the Section on Social and Emotional Development in the US National Institute of Child Health and Human Development. And he’s the editor of the 4th Edition of The Role of the Father in Child Development, just published this year by John Wiley and Sons. Now the Association of American Psychologists has described the work of Michael Lamb as having an extraordinarily significant and enduring influence on scholarship and on the conditions of children worldwide,
Michael Lamb: Well I think the general point is that fathers play an extremely important role in their children’s development, that it’s a role that serves children best when it’s initiated as early as possible in the child’s life."
https://www.abc.net.au/rn/talks/lm/stories/s1099987.htm
So, the development of a child with two "mothers" would be just the same as one with a mother and father, eh? After all, it is beyond "any doubt that parents' genders are irrelevant to children's developmental outcomes."