There is no expiation for a false oath except sincere repentance

Firstly: 

Yameen ghamoos
refers to a false and evil oath, such as that in which a person unlawfully
consumes the property of another. It is called ghamoos because it immerses
(taghmis) the one who does that in sin and then in Hell. This was stated by
Ibn al-Atheer in al-Nihaayah (3/724). 

Secondly: 

It says in
al-Mawsoo’ah al-Fiqhiyyah (35/41): 

The fuqaha’
differed concerning the necessity of expiation in the case of a false oath.
There are two points of view: 

1 – That it is
not obligatory to offer expiation for a false oath. This is the view of the
majority of fuqaha’: the Hanafis, Maalikis and Hanbalis. 

2 – That it is
obligatory to offer expiation for a false oath. This is the view of the
Shaafa’is.  

Each group
offered evidence to support its view. End quote. 

See:
Badaa’i’ al-Sanaa’i’ (3/3), al-Taaj wa’l-Ikleel (3/266) and
Kashf al-Qinaa’ (6/235). 

It says in
Fataawa al-Lajnah al-Daa’imah (23/133): 

Yameen ghamoos
is a major sin, for which no expiation is sufficient because it is such a
grave sin. No expiation is required for it according to the more correct of
the two scholarly opinions; rather what is required is repentance and
prayers for forgiveness. End quote.  

Whether one
says that expiation is required or not, the expiation does not expiate the
sin of a yameen ghamoos. Rather it is essential to repent sincerely. 

Hence Shaykh
al-Islam Ibn Taymiyah said in Majmoo’ al-Fataawa (34/139), after
mentioning the difference of scholarly opinion concerning expiation for a
false oath: 

But they are
agreed that the sin is not erased merely by offering expiation. End quote. 

Thirdly: 

A false oath,
like other sins, may be expiated by sincere repentance. There is no sin for
which repentance cannot be accepted, for Allaah has opened the door of
repentance to every sinner, and Allaah accepts the repentance of the one who
repents. 

Allaah says
(interpretation of the meaning): 

“Say: O
‘Ibaadi (My slaves) who have transgressed against themselves (by committing
evil deeds and sins)! Despair not of the Mercy of Allaah, verily, Allaah
forgives all sins. Truly, He is Oft‑Forgiving, Most Merciful”

[al-Zumar
39:53] 

Ibn Katheer
(may Allaah have mercy on him) said:  

This verse is
a call to all sinners, kaafirs and others, to repent and turn to Allaah. It
tells us that Allaah forgives all sins for the one who repents from them and
turns away from them, no matter what they are, no matter how many they are,
even if they are like the foam of the sea. There are many verses on this
topic. End quote. 

See also the
answer to question no. 46683
for more information. 

And Allaah
knows best.