This phrase has many variations with none deemed as the official, but the most common by far (at least when using Google’s ngram viewer) is little or no.
Little or no is a phrase that means something or someone has a small amount of something, if at all. Usually this is used when critiquing or criticizing something. If the object or person has it in any amount, which is doubtful, it is a very tiny amount. It is used as a submodifier
The second most popular variation is little or nothing. Still the same meaning but slightly different structure in a sentence. See the examples below.
After little or no and little or nothing, the most common variation is little to no. The change in the phrase is minor. Syntactically it is a difference between a comparison and a range. In the phrase, the meaning is still the same.
The picture looks even worse when you add to this mix a diverse population, many of whom have had little or no quality sex education and lack a basic understanding of their sexual health. [The Telegraph]
About seven in 10 say they’ve heard only a little or nothing at all about the case, King v. Burwell, which challenges a key provision of the Affordable Care Act. [The Washington Post]
In 2014 on home soil, New Zealand had little to no build-up to the world championships, and ended up suffering two defeats at the hands of eventual runners up South Africa. [Stuff NZ]