Negative Commandment #137
Sefer Ha’mitzvos Ha’Katzar (The concise book of mitzvos)
By the Chofetz Chaim
This book lists the Torah mitzvos that can be observed today
Second Section – the Negative Commandments
137. It is a negative commandment for a mamzer to marry a Jewish woman
As it states in Devarim (Deuteronomy) 23:3, "do not allow a mamzer to enter the community of G-d." A mamzer is a person who is the child of illicit relations that are punishable by spiritual excommunication, except for relations with a niddah (a spiritually impure woman) - as that child has a defective status but is not a mamzer.
Whether the child is male or female, he or she is forbidden forever to marry a Jewish person. A mamzer is allowed to marry a convert and their children have the status of mamzer.
If someone is born from an unmarried woman and she either does not say who the father is or she says, "such and such a person who is a mamzer is the father," the child has the status of a possible mamzer. Also, a baby found in the marketplace and it is not known who is the child's father or mother, the baby has the status of a possible mamzer. According to Torah law, a possible mamzer is allowed to marry into the community, but our Sages of blessed memory (Kiddushin 73a) forbid him to marry into the community. It is forbidden to marry a mamzer or a possible mamzer.
There is also a mamzer by the law of the Sages. An example is a woman who heard her husband died and remarried, and then it is found out that her husband is still alive - then the first husband has relations with the woman while she is still married to the second husband - the offspring is a mamzer according to the law of the Sages. A mamzer according to the law of the Sages is allowed to marry another mamzer according to the law of the Sages.
This applies in all places and at all times.