Abstract We report results from a study of B ± → DK ± decays followed by D decaying to the CP-even final state K + K − and CP-odd final state K S 0 π 0 $$ {K}_S^0{\pi}^0 $$ , where D is an admixture of D 0 and D ¯ 0 $$ {\overline{D}}^0 $$ states. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angle ϕ 3. The results are based on a combined analysis of the final data set of 772 × 106 B B ¯ $$ B\overline{B} $$ pairs collected by the Belle experiment and a data set of 198 × 106 B B ¯ $$ B\overline{B} $$ pairs collected by the Belle II experiment, both in electron-positron collisions at the Υ(4S) resonance. We measure the CP asymmetries to be A $$ \mathcal{A} $$ CP+ = (+12.5 ± 5.8 ± 1.4)% and A $$ \mathcal{A} $$ CP− = (−16.7 ± 5.7 ± 0.6)%, and the ratios of branching fractions to be R $$ \mathcal{R} $$ CP+ = 1.164 ± 0.081 ± 0.036 and R $$ \mathcal{R} $$ CP− = 1.151 ± 0.074 ± 0.019. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries A $$ \mathcal{A} $$ CP+ and A $$ \mathcal{A} $$ CP− have similar magnitudes and opposite signs; their difference corresponds to 3.5 standard deviations. From these values we calculate 68.3% confidence intervals of (8.5 ° < ϕ 3 < 16.5 ° ) or (84.5 ° < ϕ 3 < 95.5 ° ) or (163.3 ° < ϕ 3 < 171.5 ° ) and 0.321 < r B < 0.465.