I had committed adultery with another woman and my wife came to know about this. After that she started fighting with me demanding for divorce. Then our family members met and then everything was settled after some days she started the same topic again and again she used to fight with me. I did not tell her the truth because I knew she would leave me and go and I did not want that to happen as we have a six months old child. So one night around 2 o' clock she told me to pick up the Holy Quran and swear on it. I couldn't tell her the truth so I replaced the Quran with another book and took the swear. But the only mistake I did was I told by my mouth that I swear on the Quran but the Quran was not in my hand. My intension was not to swear on the Quran as I had already replaced it but I made a mistake or telling that I swear on the Quran. So please tell me is it a sin that I created as my Niyyat was not to swear on it as it was not in my hand. If it is a sin then what should I do so that Almighty Allaah may forgive me? Please help me.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

First of all, you have to know that adultery is a great major sin and Allaah warned us against it as He says (which means): {And do not approach unlawful sexual intercourse. Indeed, it is a Faahishah (i.e. anything that transgresses its limits; a great sin), and an evil way (that leads one to Hell unless Allaah forgives him.}[Quran 17:32]. Therefore, it is an obligation on you to sincerely repent to Allaah and avoid any means that could lead you to committing the same sin again.

If a person commits adultery or fornication, he has to conceal his sin. The Prophet said: "Whoever happens to commit any of these filthy things, should conceal himself/herself as Allaah did not expose him." [Al-Bayhaqi] Besides, it is not permissible for your wife to ask you to admit that you have committed adultery and you are not permitted to inform her even if she asks you about it. So you may use for instance Tawriyah (saying something which has more than one meaning and intending a meaning different from what the listener is likely to understand), as this is better than openly lying, and if necessary it would even be permissible to lie as it is Islamicly permissible to lie to one's wife (in certain conditions). Imaam Muslim reported that Um Kalthoom Bint 'Uqbah said:  "I have not heard the Prophet permitting telling lies in anything except in three situations: war, reconciling between people, and the talking of the husband to his wife and of the wife to her husband."

Some scholars even permitted swearing about something that is a lie if it is to achieve a considerable religious benefit or to repel a considerable harm.

Therefore, there is no harm on you for swearing while putting your hand on that book while your wife believes that you had put your hand on the Quran. There is no harm on you as well for swearing to a lie if you did so to achieve a religious benefit and you do not have to expiate for it. 

Allaah Knows best.