The verb "spit"—when used to mean "throw out saliva from the mouth"—has three forms of conjugation for tense.
spit-spit-spit
spit-spitted-spitted
spit-spat-spat
Three of them are correct for your example sentence.
But no. 1(spit-spit-spit) is not that much used compared with no. 2 and 3.
In American English, no. 1 is often used.
For 'spat', spat is also a noun and a verb as well, which means a trivial fight or have a trivial fight. As a verb, the word 'spat's past and past participle are "spatted". So it's a totally diffrent word from the 'spit's conjugations above of no. 1, 2, and 3.
After Edit
The verb "spit" has 3 kinds of past and past participle as below.
spit-spit-spit
spit-spitted-spitted
spit-spat-spat
Both no. 1 and 3 are correct for your example sentence but 2 is wrong.
In case of No. 1 and 3 conjugation, it's when they mean "throw out saliva from the mouth"
In case of no. 2 conjugation, it's when it means "to pierce something like a meat"
For 'spat', spat is also a noun and a verb as well, which means a trivial fight or have a trivial fight. As a verb, the word 'spat's past and past participle are "spatted". So it's a totally diffrent word from the 'spit's conjugations above of no. 1, 2, and 3.
So, no. 1 and 3 are correct and no. 2 is wrong for your example sentence.
But "spit-spat-spat" is more frequently used than "spit-spit-spit"
In American English, 'spit-spit-spit' is often used(not that much used).