All perfect praise be to Allah, The Lord of The Worlds, and may His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
There is no harm in obtaining identification documents for children from categories (1) and (2), but the problem lies in number (3). I will highlight the ruling of Sharia about this category as follows:
1. Abandoning one`s children is a major taboo in Islamic Sharia because the Prophet (PBUH) stated: "It is sufficient sin for a man that he neglects him whom he maintains" {An-Nasai`}. If the direct guardian abandons his duties towards these children then the ruler or the judge is authorized by Sharia to fulfill them on his behalf. The state has the right to execute whatever is beneficial to these children if their guardian failed to do so. This why the state is to be thanked for taking care of these children although, in principle, they are to be provided for by their guardians.
2. Moreover, denial of one`s child is among the grave sins because the Prophet (PBUH) stated: "There are three (types of) people whom Allah will neither speak to on the Day of Resurrection nor will He purify them (i.e., from their sins), nor will look upon them. It was said: who are they? The Prophet (PBUH) said: "one who denied his own parents, one who denied his own child and a slave who was set free by a people, but denied their favor." {Related by al-Imam Ahmad}.
Accordingly, the child born out of the wedlock bears the name of his mother, whether she approved of that or asked for it or a court verdict was issued to that end, since the child`s rights are based on it as well as those of his mother`s relatives. For example, inheritance, women prohibited in marriage and lineage traced to his mother.
Moreover, concealing the identity of the fornicators doesn`t justify denying an innocent child his/her basic legal rights. Therefore, we recommend amending article No.(9)/2001 of the Jordanian Civil Status Law by abolishing the condition where the mother is demanded to submit a written application attached with a court order to allow her to register her child in the Department of Civil Status. And Allah Knows Best.