See an attorney to determine what to do - you should be able to force an accounting and distribution.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature.
You should not be paying the mortgage from your personal funds. Upon being named personal representative of the estate, you should have given notice of the administration to all known creditors. You should also have prepared an Inventory and Appraisement listing all of your mother's property, together with its value, and filed that with the court. You should have contacted the probate referee chosen by the court when you were named as the representative, and asked them to value all of the non-cash assets such as real estate, and included those values on the inventory and appraisement filing. After paying all creditors, it was time to close the estate. You should have prepared an accounting and petitioned the court to approve it, and to approve final distributions according to the terms of the will, or intestacy.
Assuming you've been paying the mortgage out of your personal funds, you now have a complicated situation that really needs the assistance of an attorney. You are now a creditor of the estate, and you cannot be repaid for the mortgage payments you've made without permission from the court. The ultimate disposition of the house will depend on who the heirs are, and if they're amenable to working out a negotiated settlement that would let you keep the house, if that's what you want.
You need an attorney to help you.
I have an additional thought to my colleagues who have given you sound detailed advice. Adverse possession is 5 years in California. Have you been living on the property? If you have been doing it openly, notoriously and given your sister proper notice of you doing so and your intention to keep the house, then it could be yours by quieting title. Just a thought since your sister seems to have no interest for whatever reason.
You absolutely do not want to do this on your own and mess things up. You need an attorney. Just pick one in your area you like. Make sure they are California licensed and not a foreign attorney since every state has their own unique laws.
Any advice, suggestions, answers to questions, directions, either implied or express, are not binding, do not create an Attorney-Client relationship, are not solicitations but merely a generalized response or comment. The facts of every case is unique and requires carefully thought out investigation and research exclusively available during a one-on-one true Attorney-Client consultation including a signed fee agreement.
Do you have Letters of Administration? Have you done an Inventory and Appraisal on the estate? Have you cleared all of the debts of the estate and filed all taxes? Have you given notice to the State of CA? If you've done all of this, then file a final accounting and request an order for distribution. It shouldn't have taken this long and I wouldn't be surprised if the court dismissed the matter due to inaction. If you need help, suggest that you seek the services of a probate attorney who can get all of this done for you efficiently and timely.
You have received several different types of suggestions. The short answer lies with who has Letters and the legal authority to act on behalf of the estate. If that is you, you can petition the court to distribute the assets, as long as all other probate milestones have been met. Adverse possession would not apply here if the estate is in probate. Have an attorney review the probate file and advise you what to do. Good luck.