A specific recognition sequence identified by endonucleases to make cuts at specific positions within the DNA is:

Endonucleases are enzymes that cut DNA at specific locations. To achieve precise cutting, they recognize short DNA motifs that are present in the genome.

These motifs are typically palindromic nucleotide sequences. A palindromic sequence reads the same 5’→3’ on one strand as 5’→3’ on the complementary strand when the strands are aligned in opposite directions. For example, the sequence 5’‑GAATTC‑3’ on one strand pairs with 3’‑CTTAAG‑5’ on the opposite strand, which is also GAATTC when read in the 5’→3’ direction.

Because the two strands present the same sequence in opposite orientation, a single endonuclease can bind symmetrically and cleave both strands at a defined distance from the recognition site. This symmetry is essential for the enzyme’s ability to make coordinated double‑strand cuts.

Other options such as poly(A) tails, degenerate primers, or Okazaki fragments do not provide the required symmetrical pattern and therefore are not used as specific recognition sites by restriction endonucleases.

Consequently, the correct answer is the Palindromic Nucleotide sequences option.