If he lets one of his sons live in an apartment for free, is he obliged to treat the rest of his sons equally?

Firstly: 

It is essential to differentiate between maintenance and
gifts. The maintenance that the father spends on his children varies
according to their needs. What is spent on a small child is not the same as
what is spent on an older child, and the expenses of a child who is studying
at the elementary stages is not like the expenses of a child who is studying
at the University. The expenses of a daughter are not usually like the
expenses of a son. 

This includes the expenses of marriage. If a father spends on
the marriage of one of his sons, he is not obliged to give something similar
to those who are not married, because this comes under the heading of
expenses which are given only to the one who needs it. When another one
grows up he will arrange his marriage too, and so on. 

This may also be said to regard to accommodation. If the
father has a house or apartment, and the married son needs it, the father
may give it to him for him to make use of it, not to own it, and thus he
meets his need. The same applies if he needs a car for example; he may give
it to him to drive it but not to take possession of it. 

The point is that he may give each son what he needs and what
is appropriate for him. 

As for gifts which are additional to maintenance, this is
where equality and fairness is required and it is haraam to prefer one son
over the others. Sons should be given equal gifts, and each male is given a
share of two females.  

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said,
pointing out the difference between maintenance and giving: 

if we assume that one of them is at school and needs expenses
for school such as books, exercise books, pens, ink and the like, and the
other one does not need that, and he is older than him but he does not need
those things, if he gives something to the first one does he have to give
something similar to the second? 

The answer is that he does not have to do that, because being
fair in spending on maintenance means giving each one what he needs. An
example of that is if a son needs a ghutrah and cap which costs 100 riyals,
and the female needs earrings which cost 1000 riyals. What is fair? 

The answer is that what is fair is to buy the headgear for
the boy for 100 riyals, and to buy earrings for the girl for 1000 riyals,
which is 10 times more than what the boy gets. This is fair. 

Another example: if one of them needs to get married and the
other does not, what is fair? 

The answer is that he should give the one who needs to get
married and not to the other. It is to be regarded as a mistake when some
people arrange marriages for their sons who have reached the age of
marriage, and they have younger sons, so they write in their wills that the
sons who are not yet married are to have marriages arranged for them with
the costs covered from one third of the will [which it is permitted to
bequeath]. This is not permissible, because marriage comes under the heading
of meeting needs, and these children have not reached the age of marriage,
so making this will in their favour is haraam and should not be executed,
because even the heirs are not permitted to execute the will except if they
are of the age of maturity and give their consent, in which case each heir
may decide to carry out these wishes with regard to his own share. End quote
from al-Sharh al-Mumti’ (4/599). 

With regard to the obligation of treating children equally in
giving, please see the answer to question number
22169. 

Secondly: 

On the basis of the above, if a person has a son who is
married and needs accommodation, there is nothing wrong with giving him
permission to live in one of the apartments, whilst retaining ownership of
it, and he does not have to give anything to his brothers or sisters.
Similarly, you do not have to give them anything, so long as they are not in
need of accommodation, either because they are living with you and under
your care, or because the daughter is living with her husband. 

If the son does not need accommodation, then letting him live
in the apartment for free comes under the heading of giving, in which case
you have to pay attention to fairness, by giving the rest of his siblings
something equivalent to the rent of the apartment, or by making the son pay
rent which should go to you, or giving all of his siblings their share of
the rent. 

If you want to give your children ownership of the
apartments, then you have to treat them fairly and give each male twice the
share of each female, as in the case of inheritance. It is wrong to give the
apartment to the son, for example, and then tell him: Give to your brothers
and sisters, or to put it in the ownership of the males and tell them to
give to the females, because they may or may not give to them. The fact that
the son needs the accommodation — if he indeed needs it – can be met by
letting him live there, without giving him possession. If the father wants
to give him possession, then he must treat them all fairly, and it must be
documented properly in order to prevent disputes and differences between the
children. 

May Allaah help us all to do that which He loves and which
pleases Him. 

And Allaah knows best.