Varaha Purana mentions the importance of Tithis in a month and deities to be worshipped in accordance with tithis. Lord Sri Maha Vishnu is the one who explained this to Goddess Bhudevi about tithis and whom to propitiate on those days.
1. Deities to be worshipped on each Tithi
Paadyami: Padyami is the first of all the tithis. Lord Agni has to worshipped on this very first day of the month.
Vidiya: Ashwini devatas were born on this day. So, they have to be worshipped on this day. If one does this for an year it is known as Vidiya Vratam. This results in stable health.
Thadiya: Today is when the marriage of Gowri happened. Goddess Gowri has to be worshipped in this day. Girls will get married soon if Gowri Kalyanam is recited on this day.
Chavithi: This is the birth tithi of Lord Vinayaka. One can worship Lord Vinayaka on every Chavithi along with Vinayaka Chavithi.
Panchami: Panchami is the day when Nagas were born. That is why Nagula Chavithi is an important festival. One should perform rituals to Naga Devathas on this day offer milk to snakes.
Shashti: This is the birth tithi of Lord Subramanya. Lord Subramanya has to be worshipped on this day and a brahmachari has to be fed along with tamboolam. This brings success and good kids to the worshipper.
Sapthami: This is the birth tithi of Sun god. Apart from Ratha Saptami, on every Shuddha Saptami, lord Surya has to be worshipped , which gives health to the doer.
Ashtami: This is the birth tithi of eight incarnations of Goddess Durga. One can get rid of fear of enemies by worshipping Goddess Durga on the day of Ashtami.
Navami: Navami is the birth tithi of Lord Sri Rama. This day is apt for performing rituals to Sita and Rama.
Dashami: Dashami is the day on which directions came into existence. One has to worship Ashta Dikpalakas or Lords of Eight directions.
Ekaadashi: This is the birth tithi of Lord Kubera, god of wealth. Lord Kubera has to be worshipped this day which gives wealth.
Dwaadashi: This is the favorite tithi of Lord Maha Vishnu. Vishnu took the incarnation of Vaamana on this day. It is good to perform fire ritual or Homa with ghee or clarified butter on this day. One can also worship Lord Hanuman on Dwaadashi.
Trayodashi: Dharma was born on this tithi. One can worship their favourite deities on this day.
Chaturdashi: Chaturdashi belongs to Lord Shiva. Maasa Shiva Ratri falls on Krishna Chaturdashi. Lord Shiva has to be worshipped through Rudrabhisekam on this day.
Amavasya or No Moon Day: This day is very important for propitiating ancestors. It has been a tradition to offer water in the form of Tarpan to demised ancestors.
Pournami or Full Moon Day: Moon rules this day. Observing fast this whole day and propitiating Moon God in the night bestows the worshipper with unlimited wealth and mental balance in life.