"Some original Johnny Cash songs?"
Here are some original songs written in full, or in part, and recorded by Johnny Cash. However Ring of Fire, as recorded by Johnny Cash was actually a cover, as at the time, it was recorded originally by Anita Carter June Carter's sister.
“Cry! Cry! Cry!”
"Country Boy"
"So Doggone Lonesome"
"There You Go"
"Don't Make Me Go"
"Train of Love"
"Next in Line"
"Home of the Blues""
"Big River"
"A Certain Kinda Hurtin'"
"Sons of Katie Elder"
"Little at a Time"
"All Over Again"
"Smiling Bill McCall"
"The Matador"
"Send a Picture of Mother"
"Run Softly, Blue River"
"Frankie's Man, Johnny"
"I Still Miss Someone"
"Don't Take Your Guns to Town"
"Pickin' Time"
"The Gifts They Gave" *(Christmas)
"Here Was a Man" (Christmas)
"We Are the Shepherds" (Christmas)
"Who Kept the Sheep" (Christmas)
"You Beat All I Ever Saw"
"Put the Sugar to Bed"
"Girl in Saskatoon"
"Time and Time Again"
"Locomotive Man"
"Bandana"
"I'll Remember You"
"Five Feet High and Rising"
"I Got Stripes"
"Frankie's Man Johnny"
"A Certain Kinda Hurtin'"
"Mean as Hell"
"Happiness is You"
"When I've Learned Enough to Die"
"I'd Still Be There"
"What Do I Care"
"I Still Miss Someone"
"Forty Shades of Green"
"The Big Battle"
"You Remembered Me"
"Sing It Pretty, Sue"
Those I've listed are but a fraction of what Johnny Cash wrote or collaborated on, and that he recorded. Johnny Cash was also a master cover artist.