After lysis of bacterial cell whenever I went for centrifugation every time my supernatant(have protein of interest) got mixed with pellet even centrifugation at very high (g) and low temperature also.
You can use Micrococcal Nuclease (MNase) which is suitable for removing nucleic acids from cell lysates. Please go through the link below for more details on Micrococcal Nuclease.
You can use 1 M Sodium Chloride to remove DNA and nucleic acids from a cell lysate or supernatant with your protein immobilized to an affinity chromatography column. High salt works.
You can use DNAse or benzonase to reduce the prep viscosity and cut large DNA molecules after that you can add 1M NaCl to remove nucleic acid.
Alternative, you can change the PEI percentage maybe 0.05% final (first centrifuge as normal then add PEI to the supernatant at 0.05 % final stir for 20 min And then centrifuge it at 31,000 xg, 4C for 30-45 min )