• Unable to access ADC using GUI or login fails
• CLI access works with same credentials 
• Var folder is full

Follow the instrutions listed in below document to free up space in Var folder:

https://docs.citrix.com/en-us/citrix-adc/current-release/system/troubleshooting-citrix-adc/how-to-free-space-on-var-directory.html

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Problem Cause

You may have additional logging enabled which is causing huge ns.log files, for example TCP logging/acl logging,
TCP logging will be capturing all the tcp transactions and will be logging them into the system so the amount of data logged will be huge, which is creating 2GB+ ns.log file in var/log directory. also old files may present in var directory consuming extra memory.

Having /Var directory full may cause your management GUI connectivity to the NetScaler. Below is how to check and identify the issues with the same.

You may need to look how nslog parameters are configured. also determine what level of logging is required based on amount of traffic or if TCP logging is required for ns.logs.
In such scenarios it's recommended to use a syslog server to collect the logs as the TCP logs are huge and ADC has only limited memory(13 GB) How to Configure Syslog on ADC Appliance
Remove the extra data from the mentioned folders, you can remove the old traces/crashes or support bundles.

Refer to Citrix Documentation for detailed information:https://docs.citrix.com/en-us/citrix-adc/12-1/upgrade-downgrade-citrix-adc-appliance/troubleshooting.html

Unable to access ADC through SSH or SCP: CTX124664