And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith: 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 Romans 3:21, Romans 3:23 (note), Romans 3:25 (note), where this subject is treated at large.