My question is regarding tying of black strand or thread on the wrist of a newly born kid, or simply putting black (kajal) in the shape of crescent or round tip on the forehead of the newly born up to infancy at least. I have heard from the elders that it provides some kind of protection against bad sight (nazar-e-bad). There is no Qur'anic dua or supplication to be made on those threads. Just the black color is considered sufficient. Even if it has no religious basis then is it allowable to let the kids put it on in the name of social or regional custom? If it has a religious basis other than Islam then please put some light on this issue.
The practice you have mentioned has no basis in the Islamic Shari'ah. The rites of passage regarding births instituted by Islam do not include this practice. Besides, the cure from the evil too has been provided in the Qur'an. The last two surahs named al-mu'awwazatain (the two protection seekers) seek God's protection against such effects. Practices which are obviously religious in nature should not be followed even as part of culture.