On doctoral level, no tuition fees are charged, but you will need to cover your living expenses. When you apply for doctoral admission, you can ask the Finnish university department for advice on research funding options. The university departments may have paid doctoral research positions available, or doctoral funding schemes of their own. They can usually also best direct you to potential grant-awarding foundations in your field of scientific research.
The national EDUFI Fellowship scholarship programme is available for doctoral level studies and research in Finland.
Note that you can not independently apply for the EDUFI Fellowship - the "applicant" in this scholarship programme is your Finnish university department. So, in order to be eligible for the EDUFI Fellowship, you must first successfully apply for doctoral admission.
If you have questions regarding the EDUFI Fellowship itself, please contact the scholarships admins directly. You can find their contact details on the above EDUFI Fellowship web page.
Note that EDUFI Fellwships are not full degree scholarships but "start-up grants" awarded for a maximum of 12 months. After the EDUFI scholarship period the student/researcher will need to find other sources of funding.
Other funding resources
Paid Doctoral positions may also be available - see links to the universities' Doctoral info pages in the section Doctoral Admissions.