Hi,
You can use the latest JAVA version.
You just need to make sure that you follow the ASA/ASDM/JAVA compatibility matrix:
http://www.cisco.com/c/en/us/td/docs/security/asa/compatibility/asamatrx.html
http://www.cisco.com/c/en/us/td/docs/security/asdm/7_5/release/notes/rn75.html#id_25476
Regards,
Aditya
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