Yes, if you are under the age of 18, even though you purchased it and pay the monthly cost, your parents retain custody of you and your things. You can do whatever you want after you're 18, however if you're 18 or older and living in their house, they can't take it away or ground you, but they can tell you...
...however, they can't force you to get a new phone. If you don't like what another company does with its products, you can always buy another one from any other manufacturer. A limited warranty means that the manufacturer will replace damaged or malfunctioning parts—but only after you've used them for some time.
In conclusion, yes, your mother can take your phone away if you pay for it.
As long as you reside in your parents' home, are financially supported by them, and are legally accountable for you, they have the authority to make decisions about how you spend your life. They may need to keep your iPhone and return it to you when you reach the age of 18, as it is technically your property that you paid for.
Consider paying a portion of the cost yourself. Your parents would most likely appreciate the fact that you volunteered to pay for a piece of it. This will also demonstrate to your parents how determined you are to obtain this thing. Do not back out of your offer if your parents ask you to pay for half of it. Keep your word and pay the agreed-upon portion.
You are a legal adult. Your parents do not have the power to seize something that is the property of another adult. And, sure, if you purchased the phone and paid the bill, it is yours. It is a felony for your parents, or anybody else, to remove someone else's property without consent. And even if they had permission once, they can't give it to others.
However, if you did not pay for the phone (or any other item), your parents could be prosecuted for theft. Even if you agreed to pay them back later. And even if you promised not to break items when you leave home.
In addition, your parents may have certain rights as an owner and holder of the storage agreement. For example, they may be able to sell some of your belongings if there is no more room in the house for you to bring new things when you move out. Or maybe they will let you take some of the unneeded items with you if you go to school or work outside the city limits. But you should ask them first before you pack up your belongings.
Finally, if you moved out of the house when you were 18 years old but still need money every month until you turn 21, your parents are required by law to keep paying your medical bills if you become sick. They can choose not to do so, but then they would no longer be responsible for you. So it is in their best interest to keep sending the checks.
If you own the phone, your parents—or anybody else—cannot legally take it away from you. On the other hand, if your parents are paying the phone's monthly expenses, they have the right to quit doing so. When this happens, the phone company will usually send a new device to replace it.
In addition, your parents can ask the phone company to stop providing service to you by calling 1-800-331-0500 and requesting that your account be closed. However, even after you've been disconnected, your parent or guardian can go to any police station and file a lost or stolen report. This would then allow the police to continue searching for your phone.
Finally, if your phone was lost or stolen and recovered later, your parent or guardian could request that the phone company reinstate your account. You would then have access to all of its features including calling history, text messages, etc.
As long as you have a working phone number, your parent or guardian cannot forbid you from using it. If you don't want them to know where you are, tell them before they turn off your service.
You are an adult when you reach the age of 18. You are legally capable of purchasing a phone and contracting for phone service. Your parents do not have the authority to take away your phone if you have paid for it, signed a contract with the phone provider, and are paying the phone bills. At 18, you also have the ability to deny any contact from your parents or receive new information from them.
As long as you stay on your parent's plan and pay their bill, they cannot take your phone away from you. They can still access its contents through the Google Account linked to it. If you have set up a lock screen password, they would need your password to view any relevant information. However, if there is no password set, they could see everything on the device including calls made and received, texts messages sent and received, email messages, notes, photos, videos taken with the camera, etc.
If you aren't using your phone and don't pay your bill, your parents may be able to take it away from you. In this case, they would need your password to look at the device and find out how to disable it so they can send it back to the manufacturer or phone carrier.
Without your permission, your parents can't just break into your phone and read emails or take pictures without your knowledge.