How authentic is the Prophetic Hadith which states that a child conceived from conjugal relations between spouses during the menstruation period will be from the people of Lut (Sodom)?

There is no Prophetic tradition (Hadith (definition)) indicating that a menstruating woman can conceive, and medicine confirms the impossibility of a menstruating woman becoming pregnant, so there is no need for fear. As for intercourse during menstruation out of ignorance, there is no sin in it, based on the Almighty's saying: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts intended."