How can one atone for masturbating during Ramadan days, and for the feeling of remorse and despair of Allah's forgiveness?

The door of repentance is open. If you truly regret your sin and resolve not to return to it, then have good expectations of your Lord. Strive in acts of obedience and increase in good deeds to expiate your mistake. If semen was discharged, you must make up that day after Ramadan, along with repentance. One who repents from a sin is like one who has no sin, and whoever turns to Allah, Allah turns to him.