My son and I will visit Dubai. His father is working there but we are not married.
Is there any problem specially with my son if his parents were not married?
Edit (not from OP) to transfer some detail from a Comment:
Is it true that if Dubai police find out that I'm not married to my boyfriend (fiancé) they will take my child away from me?
First of all, you can travel freely with your son - there are absolutely no restrictions; neither in Dubai nor anywhere - that you must be married to the biological parent of your child in order to travel with him/her.
If you are not the biological parent or not the legal guardian, then you must carry some documentation that gives you authority to travel with the minor and act as their ward; but this is not the case with you.
Next, the issue is how are you getting into Dubai? If your fiancé has applied for your visa as a spouse then he must have shown a notarized marriage certificate.
If he is sponsoring you as a family friend then no worries at all.
If you don't need a visa (for example, you are eligible for visa free entry or are getting a transit visa or a visa on arrival), you have nothing to worry about.
Finally - Dubai police will not take away your son if the child is born out of wed lock. This is only done in very extreme and rare cases (for example, in the case of rape or abuse); and frankly I have yet to hear of this done in any GCC country (even conservative Saudi Arabia).
The only problem you have is that it is illegal for opposite sex couples to cohabitate if they are not married or otherwise related. This only comes into play if you are reported to the police; and you will only be reported to the police if you give reason for people to do so.
You may also face this hurdle if you are staying with your fiancé at a hotel; some might ask for a marriage certificate - especially if you are rowdy and give them cause to do so.
Dubai police are not going around knocking on people's doors checking marriage certificates.
If you plan to move to Dubai and live with your fiancé, then you'll have some concerns as without a marriage certificate, you and your son cannot be sponsored by your fiancé/husband - which means you cannot enjoy freedom of movement in and out of UAE, have your son enroll in school, get a driving license, open a bank account and all the sundry that one does when moving to a new country.
However, for a short visit - not a problem at all. Relax, and enjoy your trip. Depending on how old your son is, make sure you plan a visit to LEGOLAND =)
Dubai is the less conservative (or the most modern) Emirates in the UAE. You can go and visit your son's father without being married to him. Nothing will happen to you.
Indeed, as it is mentioned in a comment, the police doesn't check couples wedding certificate while you are visiting the city. You can check in an hotel and share the same room and bed with your boyfriend or girlfriend without being married together. Nobody will check if you are married or not.
The problem will mostly come if you want to establish yourself there on the long term. You need a sponsor and the sponsor will be your husband if he has a job but you don't. If you aren't married, then he can't be your sponsor. In that case, you have to find your own working contract offered by a sponsoring company.
Keep in mind that in the UAE, you have the law, the culture and the reality. According to the law, you can't live with an adult from the other sex if you aren't married. The culture is a mix of tradition and modern. Dubai has 90% of foreign people. So while local influence is visible, people aren't blind on the fact that they couldn't live without tourism and international business. As a result of that, they are pretty tolerant. As long as you show respect and you are discrete, you won't face any problem.
