Here the basical references al-Muwatta' 1, 2, 3, 4 sunan abi Dawod, jami' at-Tirmidhi 1, 2 and sahih Muslim.
The ruling among scholars is what ever makes ghusl necessary (because of marital intercourse or a wet dream) makes the punishment (for adultery) necessary. Ibn Abi Zayd al-Qayrawani said in his Risala:
Legal Consequences of vaginal penetration
- Ghusl is obligatory
- Legal consequences in case of fornication
It necessitates the hadd punishment [for zina] and the payment of the dowry and gives the married couples the status of being muhsan and makes a woman who has gone through a triple divorce halal for her original husband and invalidates hajj and fasting.
Now to make the meaning of the above narrations clear:
"When the circumcised part passes the circumcised part, ghusl is obligatory."
This means that the penis (in my understanding the glans الحشفة as this is the word used in fatwas) must penetrate (disappear fully in the vagina).
Al-Nawawi said in Sharh Muslim:
With regard to the phrase “and the one circumcised part touches the other, then ghusl is obligatory”: the scholars said: what this means is when your penis disappears into her vagina; it does not mean touching in a real sense. That is because the circumcised part of a woman is above the vagina, and the penis does not touch it during intercourse. The scholars are unanimously agreed that if he places his penis on the circumcised part and does not enter (the vagina), then no ghusl is required, neither for him nor for her. (source islamqa)
So on the whole and as far as I understood your question, your case is not subject of hadd or punishment, but you should sincerely repent and leave this sin and your co-sinner ...
Finally note that if a person commits zina he must not confess this misdeed due to:
Malik related to me from Zayd ibn Aslam that a man confessed to fornication in the time of the Messenger of Allah, may Allah bless him and grant him peace. The Messenger of Allah, may Allah bless him and grant him peace, called for a whip, and he was brought a broken whip. He said, "Above this," and he was brought a new whip whose knots had not been cut yet. He said, "Below this," and he was brought a whip which had been used and made flexible. The Messenger of Allah, may Allah bless him and grant him peace, gave the order and he was flogged. Then he said, "People! The time has come for you to observe the limits of Allah. Whoever has had any of these ugly things befall him should cover them up with the veil of Allah. Whoever reveals to us his wrong action, we perform what is in the Book of Allah against him." (Muwatta' Malik)
but if he/she confessed to an authority the punishment must be applied.
If he/she chose not to reveal his/her sin sincere repentance is always the best solution.