It is Jesus’ faith working in us who believe. So, we see that our righteousness is not IN Christ, but OF Him. And if so, we become part with Him, and He IN us.
I don't know which version you quoted, but it clearly is incorrect and out of context.
Firstly, God is faithful, and He does give us faith. Likewise, God does impute Christ's righteousness by grace to Christians for their faith. However, He expects us to use the faith He has given us.
"and be found in Him, not having my own righteousness, which is from the law, but that which is through faith in Christ, the righteousness which is from God by faith;" Phil 3:9
Note carefully, in this passage it is by faith "IN" Christ, NOT "OF" Christ as you quoted. That it is our faith Paul is referring to is proved by the verses following number 9 in this chapter. Paul uses his faith as an example.
For understanding of passages like that I don’t use a “version”, I go directly to the Greek text. Compare to this.
Matthew 11:2 Now when John had heard in the prison the works of Christ, he sent two of his disciples,
Philippians 3:9 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:
Also look here.
Galatians 2:20 I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.
In each of those verses we see it is Christ’s faith through His indwelling as seen in the above verse and others.
>> That it is our faith Paul is referring to is proved by the verses following number 9 in this chapter. Paul uses his faith as an example.<<
I beg to differ. Paul does not use his faith as an example. As seen in the above examples Paul clearly makes it plain that it is Christ’s faith that we rely on through His Spirit within us. It is not our righteousness nor is it our faith.