Hi,
As per cisco Compatibility guide version is supported .
Your PC Operating system should be updated with latest patch
and JAVA Application you need to install latest one and also exempt ASA IP from java .
ou can install ASDM using Oracle JRE 8.0 (asdm-version.bin) or OpenJRE 1.8.x (asdm-openjre-version.bin).
other part is clear you will resolve issue after this.
For your reference find below mentioned URL
https://www.cisco.com/c/en/us/td/docs/security/asa/compatibility/asamatrx.html
https://www.cisco.com/c/en/us/td/docs/security/asdm/7_13/release/notes/rn713.html#id_25472
how to add exeption in JAVA
https://www.java.com/en/download/faq/exception_sitelist.xml
If still you will face issue check in another system