“Government” used home app to authenticate a hack thru my iPhone

See -> Recognize and avoid phishing messages, phony support calls, and other scams

Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

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How to protect your Apple account and devices

Here are some things you can do to avoid scams that target your Apple account and devices.

• Never share personal information like credit card numbers, unless you can verify the recipient is who they claim to be.
• Protect your Apple ID. Use two-factor authentication, always keep your contact information secure and up to date, and never share your Apple ID password or verification codes with anyone. Apple never asks for this information to provide support.
• Never use Apple Gift Cards to make other kinds of payments. 
• Learn how to identify legitimate Apple emails about your App Store or iTunes Store purchases. If you send or receive money with Apple Pay (U.S. only), treat it like any other private transaction.
• Learn how to keep your Apple devices and data secure.
• Download software only from sources you can trust.
• Don't follow links or open or save attachments in suspicious or unsolicited messages.

How to report suspicious emails, messages, and calls

• If you receive a suspicious email that looks like it's supposed to be from Apple, please forward it to reportphishing@apple.com.1  
• To report a suspicious SMS text message that looks like it's supposed to be from Apple, take a screenshot of the message and email the screenshot to reportphishing@apple.com.
• To report spam or other suspicious emails that you receive in your iCloud.com, me.com, or mac.com Inbox, send them to abuse@icloud.com.
• To report spam or other suspicious messages that you receive through Messages, tap Report Junk under the message. You can also block unwanted messages and calls.
• Report scam phone calls to the Federal Trade Commission (U.S. only) at reportfraud.ftc.gov or to your local law enforcement agency.

If you get a suspicious phone call or voicemail

Scammers use fake Caller ID info to spoof phone numbers of companies like Apple and often claim that there's suspicious activity on your account or device to get your attention. Or they may use flattery or threats to pressure you into giving them information, money, and even Apple gift cards.

If you get an unsolicited or suspicious phone call from someone claiming to be from Apple or Apple Support, just hang up.

You can report scam phone calls to the Federal Trade Commission (U.S. only) at reportfraud.ftc.gov or to your local law enforcement agency.

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To keep your Apple ID account secure, see the following Apple articles: 

If you think your Apple ID has been compromised

If you think your Apple ID has been compromised - Apple Support

See who has access to your device or accounts

See who has access to your iPhone or iPad – Apple Support (UK)

Delete suspicious content from your devices

Delete suspicious content from your devices – Apple Support (UK)

Check your Apple ID device list to see where you're signed in

Check your Apple ID device list to find where you're signed in - Apple Support

• if you see devices that don't belong to you, delete from your account.

Personal Safety User Guide -> Personal Safety User Guide – Apple Support (UK)

Manage and use your Apple ID -> Manage and use your Apple ID – Apple Support (UK)

(if you haven't already done this) Two-factor authentication for Apple ID -> Two-factor authentication for Apple ID - Apple Support

Change your Apple ID password -> Change your Apple ID password - Apple Support

• Create a strong password for your Apple ID, It is best if your password consists of eight or more characters and include upper and lowercase letters, and at least one number. You can also add extra characters and punctuation marks to make your password even stronger. 
• Never provide your password, passcode, security questions, verification codes, recovery key or any other account security details to anyone else. Apple will never ask you for this information.

Then see this Apple article: What to do after you change your Apple ID or password

What to do after you change your Apple ID or password - Apple Support

Never jailbroken your iPhone.