Saptamee on Sunday - Vijayaa Saptamee Vrat
Although all Shukla Saptamee belong to Soorya, still there are seven Saptamee - Jayaa, Vijayaa, Jayantee, Aparaajitaa, Mahaajayaa, Nandaa and Bhadraa which are very dear to Soorya Bhagavaan. If Shukla Saptamee falls on Sunday, it is called Vijayaa Saptamee. Any Daan, Snaan (bath), Hom, fast, worship done on that day destroys all sins. In this fast, eat only once in the evening on Panchamee; eat only once in the night on Shashthee and do not eat at all on Saptamee; and do Paaran on Ashtamee." Method of the Vrat and worship on Jayaa, Jayantee, Aparaajitaa, Mahaajayaa, Nandaa and Bhadraa Saptamee, are given in Bhavishya Puraan p 115-119.
[ Bhavishya Puraan, 1/15]

Method of the Vrat and worship on Jayaa, Jayantee, Aparaajitaa, Mahaajayaa, Nandaa and Bhadraa Saptamee, are given in Bhavishya Puraan, p 115-119.

Other Saptamee Vrat - Kaamadaa Saptamee, Paapnaashinee Saptamee, Sooryapad-Dwaya, Sarvaapti Saptamee, Maartand Saptamee, Anant Saptamee, Avyang Saptamee, Tri-Praapti Saptamee (noble birth, health, wealth), are given here in Bhavishya Puraan, p 125-128.

Saptamee on Sunday - Aaditya Shayan Vrat
On any Saptamee, 7th, when there is Sunday with Hast Nakshatra, or Soorya Sankraanti, worship Soorya Bhagavaan.
[Padm Puraan, 1/15, p 83-85]

Putreeyaa Saptame Vrat - Year-long
This Vrat is done by women, starting from Margsheersh Shukla Saptamee for 1 full year, as its name says, gives them son.

Rahasya Saptamee (Shukla Saptamee) - Year-long
This is Soorya Vrat. On this day, Shukla Saptamee, one should not even touch oil, avoid blue colors. Start this Vrat from Chaitra month, worship Soorya with 12 names in subsequent 12 months
[Bhavishya Puraan, 1/13]

Bhaadrapad Shukla Shashthee - Phal Saptamee
This is Soorya's Vrat. He is pleased even with offering flowers only. If flowers are not available one can use even tender leaves or tender grass. Anybody can worship him.
[Bhavishya Puraan, 1/13]

Maargsheersh Shukla Saptamee - Aparaajitaa Saptamee
One should keep fast on Margsheersh Shukla Saptamee and Soorya should be worshipped on this day.
[Bhavishya Puraan, 1/10]

Paush Saptamee - Ubhaya Saptamee
Keep fast on both Paush Saptamee, eat wheat flour food and milk, worship Soorya three times. Bathe Soorya with Ghee on 2nd Saptamee, offer Laddoo, cooked milk and food in Naivedya, and feed 8 Braahman.
[Bhavishya Puraan, 1/20]

Maagh Krishn Saptamee - Sarvaapti Saptamee Vrat
This Vrat is done on Maagh Krishn Saptamee. This fulfills all desires.

Maagh Shukla Saptamee - Soorya Saptamee
On Maagh Shukla 7th. This is called Raajaa Saptamee also. It is supposed to be the birthday of Soorya.
Offer your prayer for your family (Sun = in 5th House of Kaal Purush = Aries Lagna), and
Health - Sun as sustainer of life on Earth, past Karm, Aatm Shuddhi etc.
One should draw a 8-petal or 12-petal Kamal and worship Soorya on it. This Vrat takes away all sorrows of a person.
If this Vrat is done on Bhaadrapad Shukla 7th and Aaditya is worshipped on that day, one attains all desired things.
If this Vrat is done on Paush Shukla 7th, and Soorya Dev is worshipped on that day, one's all sins are destroyed.
[Agni Puraan, 20]   [Bhavishya Puraan, 1/10]

Phaalgun Krishn Saptamee - Nand Saptamee Vrat
It is observed on Phaalgun Krishn Saptamee.
[Agni Puraan, 20]