The 55-year-old shared Kira with tennis star Lisa Bonder – though Lisa insisted her husband of 28 days Kirk Kerkorian was the father, the billionaire used a private detective to discover he was not Kira's dad.
Daily Mail reports that Kira is fighting for control over Steve's estate, which is valued at $337,000 (approximately $464,000 AUD) as it doesn't include properties.
Steve took his own life in June, days before the anniversary of his 28-year-old girlfriend Allexanne Mitchum's death from a drug overdose.
The movie investor received a $600 million inheritance from his grandfather, who struck it rich in real estate, when he turned 18.
He then had his will drawn up in 2001, before he knew about Kira and while Liz was pregnant.
In the will, he noted that Liz was expecting a baby and wrote, "Whether or not such child is mine, it is my intention not to provide in this Will for such child (or any other child as to which I may be the father) in this Will or for the offspring of any such child or children, whether now living or hereafter born."
However, despite excluding Damian and Kira from his will, Steve later formed relationships with his children and actually fought to have them included in their grandfather's trust.
He successfully fought the case and ensured Damian and Kira would be beneficiaries.
Kira is now attempting to be made administer of her late father's estate so she can fight a $7 million lawsuit between Steve and entrepreneur Matthew Khoury's company KRE Wellness.
The lawsuit comes from an agreement made in 2015. Matthew claims Steve failed to pay "qualifying receipts" and filed the suit against him in April. A judge will rule on the matter this week.
Following Steve's death, Liz took to Instagram to share a tribute to her former boyfriend.
She wrote, "I am saddened beyond belief that my ex Steve is no longer with us. It is a terrible end. Our time together was very happy and I’m posting these pictures because although we went through some tough times, it’s the good, wonderful memories of a sweet, kind man that matter.
"In the past year we had become close again. We last spoke on our son’s 18th birthday. This is devastating news and I thank everyone for their lovely messages."
Damian also took to Instagram to thank his followers for reaching out with their condolences, "Thank you from the bottom of my heart to everyone that has reached out following the devastating news.
"I’m trying to reply to as many of you as I can, but please know I will always remember your kindness. This is a very strange and confusing time and I’m immensely grateful to be surrounded by my phenomenal family and friends."
While he wasn't as close to Damian and Kira as he perhaps could have been, Steve reportedly did want to have children with his former girlfriend Allexanne according to her aunt, Carrie.
Taking to Facebook, she wrote, "Steve had two children and while he fought for them, they were unplanned.
"Steve didn’t want to be a bad father, as he claimed his father was, so I was surprised he wanted to be a father but he told me Allexanne was afraid of being left alone if he died, since he was 25 years her senior."