At this time you have the latest update for your S3 Neo. If you were to force an update past that it may throw in some technical issues alongside it. The phone wasn't necessarily made to handle anything past Android 4 there's a lot of technical limitations.
Hope this answers your question!
Be sure to click " ✓ Accept as Solution" when you find an answer that works for you.
based on the model that you indicated on your post you can upgrade up to 4.4.4 Android KitKat
but it also depends on your carrier if they pushed the update you can try this method to update your device.
For the OTA method
Software update via Smart Switch
Not only is Smart Switch great for transferring data, but it’s also an easy way to update your phone’s software. When you open Smart Switch on your Mac or Windows PC, you’ll see an option to update to a new software version if one is available.
First, make sure your phone is charged to at least 20% before proceeding. Connect your phone to your computer using the USB cable provided with your phone, and then open Smart Switch on your computer. If a software update is available, Smart Switch might automatically prompt you to update the software or will display an option to Update. Click Update and follow the on-screen prompts to download the necessary files and complete the update process. Keep in mind your phone might turn on and off during the update process.
Note: Don't disconnect the USB cable or use your phone until the update is complete.
hopefully, this will help with your problem
Be sure to click " ✔ Accept as Solution" When you find an answer that works for you