Greetings Fellow SharePoint users,
As a SharePoint 2010 and 2013 administration I have had to give users exclusive access to sub-folders in a document library often. I understand your struggle. In 2013 the Look and Feel has changed significantly and it took me a while to figure out the proper steps to manage sub-folder permissions. Once I figured it out I wrote down the below steps with screenshots which I am now sharing with you.
 
In this example, I have a simple SharePoint 2013 Web App setup and am creating the below Document Library in it.
 
 
• Click on the Settings Icon (which looks like a wheel) to the top right of the page.
 
• In the Drop-Down list choose Site Content. 
  
• Click on add an app icon as show above.
 

 

• Click on Document Library icon as shown below.

 

• Click on the Advanced Options as show below.
 
• Add a Name and choose the Document Template as None. Below is a screenshot.

 
 
• Go to your new document library. On the top of the page you should see Browse, Files and Library as show below.
 
• Click on Files. You should see a new horizontal ribbon as shown below.
 

• Using the New Folder button, create your desired folder(s). Below is what you should see once the folders are created.
 
• Go back to the home folder which in our example is Test Document Library.  On the top ribbon, click on Library and then choose Library Settings as show below
 

 

 

 

• Now you will be in the Settings page. Under Permissions and Management, click on Permissions for this document library as show below

 
 
• Currently you should see that this document library is inheriting permissions from its parent.
 
• Click on the Stop Inheriting Permissions option. Click OK on the Message.
• Now you should see that this document library has unique permissions.

 

• In my example I am going to remove all the current users and groups (except for myself) and add three specific users. Use the Remove User Permissions to remove users and Grant Permissions to add users.  You will see the below

 

• Now I am going to break the permission inheritance of each sub-folder. Go back to your new home folder, click on '…' then click on '…' and choose 'Shared With' for Folder1

 

 

• You will now see the alert has changed. Click on Stop Inheriting Permissions. This will stop the Folder1 from inheriting permissions from the root folder.
 

• Click OK when you see the below message
 
• Now I am going to remove User2 and User3. This way only me and User1 will have access to Folder1. After I make the changes below is what I see. Notice the alert message has changed.

 

• Lets do this again for Folder2. Go back to the root folder i.e. is Test Document Library , click on '…' then click on '…' and choose 'Shared With' for Folder2
 
 



 
 

• Notice that Folder2's access permission doesn't match Folder1 this proves that Folder1 has exclusive access. You will also see the below alert. Click on Stop Inheriting Permissions. This will stop the Folder2 from inheriting permissions from the root folder.
 



 
 
• Click Ok when  you receive the below message
 
• Now I am going to remove User1 and User3. This way only me and User2 will have access to Folder2. After I make the changes below is what I see. Notice the alert message has changed.
 

• You can follow the same steps mentioned above to give User3 exclusive access to Folder 3. Now we test the permission settings. I am going to log into the Web application as User1
 
 
 

 
 
• Go to the document Library that you have built. In my example I am going to Test Document Library. Below is what I see
 
• Just to be sure, I have logged in as User 2 and User 3 and below is what I see.

 

 

I would like to point out that breaking the inheritance permissions of sub-folders can get confusing over the period of time. I'd rather create separate document libraries.

Hope this helps!