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.
If the sun shines for 24 hours a day in your country and never sets, then you should fast and break the fast according to the timing of the nearest country to you where the sun rises and sets; this applies to obligatory and supererogatory fasting.
However, if the fasting person finds hardship in fasting to an extent that he is unable to continue the fasting due to the extreme length of the day, then it is permissible for him to break the fast according to the necessity only [and not eat his fill] and then make up for that day whenever he is able to do so. As regards supererogatory fasting, one is not obliged to make up for the day he broke the fast.
For more benefit, please refer to Fataawa 83637 and 89463.
Allaah Knows best.