Mom has been AL for a short time. She insists one on the residents hates her and is arranging bad things. For example she says she arranged for my mother to get inferior food. To move to a bad table. She also is sure this woman and her husband are the owners. She says she's crying all the time and that she's being abused by this woman.
If your mom hasn't been diagnosed with dementia it might be prudent to take her to see her Dr. Delusions are not normal age-related decline.
In the meantime, try to redirect your mom when she starts talking about this resident. Compile a list of subjects in your mind if you have to. As soon as your mom starts talking about the other resident interrupt her and say something like, "Oh mom, you just reminded me, would you like me to pick up lunch and bring it over on Tuesday? I thought we could have lunch together." Or whatever is appropriate for the situation.
If you get the sense that your mom is about to go into stories about this other resident tell her a funny story, something that happened to you, or someone in your family.
Redirect, redirect, redirect.
Try not to argue with her by insisting that this other resident is not out to get her. To your mom it's very real. And if your mom truly believes that this person is abusing her that is very scary for your mom.
During times when your mom isn't talking about this resident let your mom know that you're there for her and that you'd never let anything happen to her. Provide her comfort and reassurance.
These are the suggestions I'd make if your mom has dementia. If she doesn't have dementia then you may be able to reason with her but paranoia is like a brick wall, it's difficult to get around.
As a last resort maybe your mom's Dr. can prescribe anti-anxiety medication for your mom although you might end up with a mom who's sedated AND paranoid.
Often the person with dementia has delusions about perceived slights, thefts, and wrongdoing against them. You can read on this site about some ways to handle those, but most say don't try to convince her she's mistaken. Just redirect, change the topic and comfort her by saying that all is well. If my cousin is alarmed or worried, I tell her that I have taken care of everything and all is well. That seems to bring her great relief. I don't try to convince her that she is wrong.
I would give it more time in the AL. If she is having these symptoms there, she could also have them at home. Many family members report this.
Another thing that I did when my cousin first went to AL was to tell her that other residents and the staff had told me how much they liked her and that she was very pleasant and kind and it was a joy to have her as a new resident. I told her this to make her feel more welcomed, even if it wasn't always true. Your mom may not remember these comments, but they may help her feel better in the moment.
You might also help create a reason to celebrate in the AL. Is her Birthday coming up. They normally have a big Birthday party for everyone who has a birthday that month. You might get involved with that, bring balloons or treats for all those celebrating their birthdays. Explain that they are from your mom. That might help her feel good about her contribution. Giving feels so good for people, imo. I try to ensure that my cousin is able to give to others in her facility.
My cousin was very resistant in regular AL and too scared to join in, so I discussed it with the activity director and she encouraged my cousin to help her with some things before the activities, like handing out papers and supplies to the other residents. It was a simple job, but it really made my cousin feel needed and special. Her mental abilities caused her to not be able to do for long, but it was great while it lasted.
since you say your mom is in AL and not memory care it doesn't sound like your mom is witnessing strange behavior to make things worst
I'd be careful of added drugs due to the many risks including risk of falls - I do allow a small dose of seroquel at bedtime