When deceased requested no funeral service?

One problem with a funeral is that it's public, not by invitation. An option is to have a party, and perhaps have one person make a short speech of welcome and refer to the deceased.

My second parents-in-law moved into a NH and FIL died 3 weeks later at 90 from an accident on his scooter (he was the healthier of the two). The law required an autopsy (and in fact his new doctor had probably stuffed up a medication). FIL dearly wanted his body donated to medical research (he was an exPOW with various continuing results), but it couldn’t happen because of the autopsy. We had a party at the big room in the NH and my DH (the oldest son) gave a short speech. All the family were happy with that. My daughter very kindly came with her 3 week old baby, which was a wonderful 'life goes on' reminder.

MIL lived to 97, all of her generation were dead, and the sons decided to skip the party. She was cremated without a service, they collected the ashes, mingled them with FILs ashes kept in an urn, and joined together to scatter them in the sea. No-one objected.

My first MIL, who I loved dearly, had a ‘real’ funeral. The bulk of the attenders were the family of my ex’s partner, who she did not like much. When I got there, I wondered if I was in the wrong funeral until I actually saw my ex. They all made speeches which were more or less hypocritical (sometimes highly hypocritical). It turned my stomach. I didn’t go to my ex’s funeral, although we were by then on good terms, because I couldn’t face the same people again. My (and ex’s) daughters couldn’t keep them away, even though the relationship had broken up.

Do what works for you. Make a good memory for yourself, and for the people you care about. It doesn’t matter to the deceased.

I wish people would understand, A funeral isn't for them. It's for their loved ones to say goodby. For closure. You are already gone so why should you care if they give you a funeral or not? So don't put that on them. Give them closure they need and want and leave it at that.

A friend died years ago and didn’t want, and couldn’t afford, a funeral. He left an amount of money that his family used to throw a party at his favorite bar. They brought all of his photos for guest to go through and take what they wanted. It was a lot of fun talking a new laughing and remembering our friend.

Your mother is not deceased and has not made any formal statement about her wishes. You are crossing a bridge miles before you get to it.

If she does choose to give you instructions - and don't badger her about it, it's in poor taste - follow them (and without looking for loopholes, by the way).

If she doesn't, then her executor or her next of kin if there is no executor should make the arrangements s/he thinks best.

Imho, while your question is valid, oftentimes things change. You've even stated that your mother may want to have some kind of service. Have some kind of plan, while also being aware that it would be amended.

There must be something about a traditional funeral service that she doesn't like. I would try to find out SPECIFICALLY what there is about a funeral service that bothers her. Is it something a clergyman might say? Is it something about what attendees might do or say? Is there some part of a "traditional" funeral that turns her off?
As noted by others, the funeral or memorial service is mainly for the benefit of friends or family. It helps them heal. Remind her that many people would just like to have a way to say "goodbye". Is there anything she could suggest?

No one would want to include something the departed would find disagreeable. If she doesn't want clergy, OK Mom, we don't need clergy. If there is some kind of music she objects to, OK Mom, we don't have to have that. Flowers? Not necessary. A number of traditional trappings could be dispensed with. A bit of gentle questioning of your mother might suggest some ways to mark her passing in a dignified, sensitive way that she would not find objectionable.

My mom or Aunt did it have a furenal I don’t want one either cause I will be the only one left so who is going to come and visit me no one we are a three person family that’s it just us well me and my dad know but I don’t want one

Simple service at crematorium followed by notice in relevant paper and letters to those who would want to be informed of her death saying "private " service has taken place.