Hi,
Yes ASA does support QoS and your requirement can be fulfilled.
You can prioritize the particular traffic that you want.
Please review the below links for more understanding on QoS :
https://supportforums.cisco.com/document/7011/asa-qos
http://www.cisco.com/c/en/us/support/docs/security/asa-5500-x-series-next-generation-firewalls/82310-qos-voip-vpn.html
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Pulkit