My mom is paranoid and thinks people are coming to get us. She is so anxious, how can I calm her down?

Is she taking an anti-anxiety medication? If no then get her to the doctor so the doctor can prescribe one.

If yes, it might need to be adjusted as the above poster suggested.

When she is anxious try dimming the light in your house. Turn off the TV. Decrease as much stimulation as you can.

Sit with her and talk in slow, soothing tones. Hold her hand. Offer her some ice cream or another treat. Make sure she's hydrated, clean, warm/cool enough.

If her anxiety is something new she'll need to see the doctor.

Get her checked title a uti if this is new behavior. Call her doc for med adjustment, which should be evaluated at least twice a year.