I am making an app that takes photos from web site for some Username and shows it in a UITable with username then when clicking user name it shows photos for this user and t
You can simply store UIImage objects in CoreData directly, just use Transformable data type, and you are ready to go
First, always store your images in a usable format such as PNG or JPEG instead of NSData. This will save you a lot of headaches.
Second, the rule for storing binary data is:
1mb store on disk and reference it inside of Core Data
The storage inside of Core Data should be binary and you can write accessor methods for it. Take a look at this answer: Core data images from desktop to iphone
The example code I linked to describes how to create accessors in your NSManagedObject subclass that will convert the image back and forth between a UIImage and binary data.