The scenario you've described is known as a silent mutation or synonymous mutation. In this type of mutation, a substitution in the DNA sequence leads to a new codon that still codes for the same amino acid as the original codon due to the redundancy of the genetic code.
The most likely effect of this mutation is that it will have no significant effect on the protein being produced. Since the amino acid sequence remains unchanged, the overall structure and function of the protein are expected to be unaffected. Therefore, in many cases, the organism may not exhibit any noticeable changes as a result of this mutation.