The scintillation index of focused higher order laser beam propagating in non- Kolmogorov atmospheric turbulence is formulated by employing the Rytov method and the equivalence of the structure constant. Our evaluations are performed for even modes. The equivalence formula for the structure constant is extracted from our earlier work in which the equivalence is obtained by equating the scintillation indices found in the Kolmogorov and the non-Kolmogorov turbulence. If not specified otherwise, the focused beam is defined when the focal length is equal to the link length. For the focused higher order laser beams, as the power law exponent of the non-Kolmogorov spectrum decreases, the scintillations decrease. At any power law exponent, the scintillations tend to become larger when the mode order of the focused beam becomes larger, i.e., the focused Gaussian beam is advantageous over the focused higher order laser beams for any realization of the non-Kolmogorov turbulence. Again being valid for any power law exponent, increase in the source size is found to decrease the intensity fluctuations of all the focused higher order mode scintillations. Especially for the larger order beams, focusing the higher order beam at a distance smaller than the link length results in a change in the be- haviour of the scintillation index versus the power law exponent. In such cases, the scintillations are observed to increase. Comparison of the focused higher order beam scintillations with the previously obtained collimated higher order beam scintillations yields that the focused higher or- der beam scintillations are lower. Collimated higher order beams exhibit lower scintillations than the collimated Gaussian beams whereas this is reversed in the focused case. Another observation in such comparison shows that the difference of the intensity fluctuations between the Gaussian and the higher order beams are much larger in the focused case, especially at larger power law exponent values.