You don't have much control over who follows your Twitter account unless you make it private. There is no official way to remove a follower from your account, but you can block certain followers from your Twitter feed by blocking and then unblocking them. That way, they will be removed from your followers list without being notified.
Steps
Method 1 of 2: Using a mobile device

Step #1. Tap on the Twitter app

Step #2. Tap on the 'Me' tab
This is the icon in the shape of a person that you can find in the bottom right corner of your screen.

Step #3. Tap on 'Next' option
You'll find this option above the Tweets, Media, and Likes options near the top part of your screen.

Step #4. Tap on a follower you want to block
By doing that you will see the person's account page.

Step 5. Tap on the gear icon
You can find this option to the right of the follower's profile picture.

Step 6. Tap on 'Block (Username)' option

Step 7. Tap 'Block' to confirm
You have now officially blocked the follower in question.

Step 8. Tap on the red icon that says 'Blocked'
You can find this option in the top right corner of your screen.

Step 9. In the pop-up menu that appears, tap 'Unblock'
The follower should now be unblocked, but will no longer be following your account.
Method 2 of 2: Using a computer

Step 1. Go to your Twitter page
If you are not already logged in, you will need to enter your password and the email address you used to register with Twitter (or your phone number or username).

Step 2. Click on 'Next' option
This option can be found on the left side of your Twitter feed, just below your profile image and background image.

Step 3. Click on the 'More user options' button for the follower in question
This button can be found to the left of the 'Follow' (or 'Follow') button in the information box for a particular user.

Step 4. Click on 'Block (username)' in the drop-down menu

Step 5. Click on 'Block' again to confirm your choice

Step 6. Click on the 'Blocked' button
This button can be found in the top right corner of the profile of the follower in question. After clicking on it, it will no longer be blocked, but will no longer track your account.
Tips
- There are several ways to go to a user's profile to block them, including clicking or tapping the follower's name in your Twitter feed or searching for the username in Twitter's search bar.
- Blocked users will not be able to contact you in any way on Twitter.