Adam Clarke on Philippians 3:9

And be found in him - Be found a believer in Christ, not having mine own righteousness - not trusting in any thing I have done or could do, in order to my salvation; relying on no scheme of justification, set up either formerly by myself or by others.

But that which is through the faith of Christ - That justification which is received by faith through the atonement made by Christ.

The righteousness which is of God - God's method of justifying sinners through faith in his Son. See the notes on Rom 3:21, Rom 3:23 (note), Rom 3:25 (note), where this subject is treated at large.