Is it permissible for a young Muslim man residing illegally in Europe to give his name to a child who holds the nationality of that country in order to obtain residency, knowing that the child will live with his real father, and that his intention is to provide a home for his parents?

The fundamental principle regarding residing in disbelieving lands is prohibition, except under certain conditions: safety from temptation (fitnah), the ability to perform the rituals of the religion, and the existence of a necessity or dire need that necessitates it. While providing housing for one's father is a noble intention, it should be done through permissible means and in Muslim lands where provision is available, bearing in mind the Hadith (definition): "Indeed, the Holy Spirit breathed into my heart that no soul will die until it completes its term and receives its full provision. So, fear Allah and be good in seeking provision. And let not any of you be deterred by the delay in provision from seeking it through disobedience to Allah, for Allah Almighty's bounty cannot be attained except through His obedience." It is not obligatory for the son to provide outright ownership of a dwelling for his father; renting suffices. Furthermore, spending is not obligatory unless he possesses the means. It is not permissible to attribute someone else's child to yourself due to the falsehood involved and its contravention of Allah Almighty's command: "Call them by [the names of] their fathers; it is more just in the sight of Allah." This also leads to future problems, mixing of lineages, and loss of rights.