If you are in pray and have predominance of sputum (Spit) in Prayer than what is instructions in Islam and Hadith for it. Please read this Hadith on predominance of sputum in Pray.
Narrated Anas:
The Prophet saw expectoration (on the wall of the mosque) in the direction of the Qibla and scraped it off with his hand. It seemed that he disliked it and the sign of disgust was apparent from his face. He said, “If anyone of you stands for the prayer, he is speaking in private to his Lord, (or) his Lord is between him and his Qibla, therefore he should not spit towards his Qibla, but he could spit either on his left or under his foot.” Then he took the corner of his sheet and spat in it, folded it and said, “Or do like this.”
The last prophet PBUH has made all kinds of ease by his actions at the time of need due to the upcoming situations. Since today mosques are paved and the floor is also paved, so you have to keep this Sunnah in mind that you should spit into a handkerchief when necessary and keep a special handkerchief for this purpose. Last prophet PBUH gave every kind of convenience by your every action. I wish Muslims would understand and make this good practice the goal of life.