Which type of mutation is responsible for new variations of a trait?

Frameshift or missense mutation.

A frameshift mutation is a genetic mutation caused by indels of a number of nucleotides in a DNA sequence that is not divisible by three. Due to the triplet nature of gene expression by codons, the insertion or deletion can change the reading frame, resulting in a completely different translation from the original. 

The type of mutation that is responsible for new variations of a trait is the point, missense mutation.

A mutation is any alteration in the nucleotide (DNA) sequence of the genome of an organism.Mutations can be divided into somatic (body) mutations, which cannot be inherited, and germinal (gamete) mutations which can potentially be inherited and thus contribute to the genetic variation in a population.A missense mutation is a single nucleotide mutation (single nucleotide polymorphism) that generates in a different codon, which codes a different amino acid. Since a missense mutation is a single nucleotide polymorphism, it is also called a point mutation.

In consequence, the type of mutation that is responsible for new variations of a trait is the point, missense mutation.

Learn more in:

link