I'm so sorry that you are in this position.
You can certainly resign as agent under your mother's power of attorney by sending to your mother a written note indicating that you have resigned as agent as of a certain date. From that date on you will have no authority to act as her agent unless she re-appoints you by a different written power of attorney.
However, this doesn't seem to me to be a good result - - - unless your health compels you to do so. I would recommend that you offer to meet with your mother and her attorney to seek mediation of whatever concerns your mother may be experiencing, and hopefully, to work out a solution where your mother will be able to feel safe in relying upon your ability to assist her. If she has no attorney, then you should offer to meet with her with an attorney of her choice and make clear that the attorney is representing your mother. This is not a situation in which an antagonistic confrontation will benefit either of you - - - but particularly your mother.
Of course, I recognize that your mother's dementia and/or paranoia may preclude her ability to make a rational decision with respect to your offer. But in fairness to your relationship with her, and with respect to your mother, I recommend that you lend every effort to try to seek reconciliation on terms that your mother will deem to protect her perceived interests.
One possible alternative would be to have your mother create a revocable living trust that would hold all of her assets. She could name a trusted third party, or even a financial institution, as the trustee of the trust. This would provide financial management and safety for all assets owned by the trust, as well as protection from improvident actions that your mother might be inclined to take from time to time.
Such a strategy would also relieve you of the continual conflict between yourself and your mother over the protection of her assets, and decisions which you believe may be detrimental. You could be freed up to focus your efforts on her personal care and health care arrangements - - - if she was willing to allow that.
If she needs assistance with those arrangements, she can also retain independent persons (perhaps a Geriatric Case Manager) to manage her care and advise her on these subjects.
If your mother is not willing to engage in such a conciliatory response, and if her condition continues to deteriorate to the point that she is unable to adequately manage her financial or health care needs, or if she engages in conduct that is detrimental to her health or financial well-being, then you may have no recourse but to seek legal counsel on your own to initiate a guardianship proceeding against your mother. In a guardianship proceeding the Superior Court will make a determination of whether your mother is able to adequately make personal, financial or health care decisions. If not, then the Court will appoint a person with authority to make such decisions as may be needed for your mother and terminate her authority to make such decisions for herself.
This is a costly litigation proceeding in which your mother will be aware of the position that you have taken, and will have legal counsel appointed to represent her interest. So if your position is not upheld by the Court, it can be very detrimental to your ability to maintain a normal relationship with your mother.
I hope that your mother will be willing to seek a conciliatory response within the safety of her own legal counsel's office.
Once again, I'm sorry that you are being called upon to help your mother under these circumstances. I commend you for your caring attitude.