The interpretation of the role of dark matter in the Universe depends on the model of dark matter under consideration. Some models assume for example that dark matter is confined inside compact stars. In this case you can consider the presence of dark matter everywhere.

some standard model which explained the signature of dark matter indirectly . " indirectly means we can observe the effect of its presence . that effect were seen in the halos of milky ways , its stars motion , lensing ...infact through this model , presence of local dark matter were explained too. (in our solar system) . its distribution might not so good and its density would be very small per cc . may be still due to the lack of highly technological civilisation its sign cant be shown everywhere.

i think its presence is not only outside the galaxy , might be anywhere in the universe ..

It is densest within the galaxy and becomes thinner outside. The approximations to the profile can be seen in these articles:

https://en.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile

https://en.wikipedia.org/wiki/Einasto_profile

The profile is related to the Virial Theorem.

The dark matter inferred from rotation curves of spiral galaxies (assuming Newtonian gravitation) is seen from observations to be dominant in the external parts because the ratio of the local gravitational mass (deduced from the rotation curve) to the mass detected by other means (stars, gas, dust) increases with the distance to the galaxy centre. Since the nature of dark matter is still unknown (otherwise it would not be called dark matter), every dark matter candidate (such as WIMPs, MACHOs, cold gas, black holes) or alternative gravitation theories should provide and explanation why the dark/observed matter ratio increases with radius.

A related fact that is rarely discussed is that the dark/neutral-atomic-hydrogen ratio is rather constant in individual spirals (Bosma 1981), which was a motivation for us to investigate the possibility to hide baryons with very cold molecular hydrogen (Pfenniger Combes 1994). The detected atomic gas (H) would be only the visible phase of hydrogen most of the time in the form of dense molecular gas (H2) at very low temperature (3-7K).

In the mean time the amount of detected cold gas has doubled (the so-called "dark gas") but is still insufficient to fully explain the rotation curves. Another hint that undetected molecular gas exists in the outer atomic gas disk is that meanwhile a very faint population of forming stars has been detected in the UV. Since stars form from molecular gas, not atomic gas, some additional undetected molecular gas must exist in the observed atomic gas disks.

"Why so called dark matter is outside the galaxy?"

Most dark matter models propose a very large amount of dark matter. A few galaxies are thought to have little or no dark matter. Based upon observed velocity rotation curves for most spiral galaxies at least 80 to 98% dark matter is needed to bring the rotation curve anywhere near what is being observed. The Milky Way, for instance, is thought to have 30 times more dark matter than observable matter for its rotation curve to come anywhere near what is observed. That is only 3.3% observable matter. Naturally most of this dark matter must be outside the observable galaxy if matter were distributed according to the inverse square law of distance from the galactic center which is the dark matter model most often used.

There is only one well-known group of alternatives to dark matter for spiral galaxies. These are changing-strength-of gravity models like MOND. There are dozens of these proposed models but few alternatives can also explain the excess rotation rates of galaxies in a cluster, the excess bending of light (gravitational lensing), or motions of galaxies as a whole in the observable universe, without also proposing vast quantities of unseen matter. For this it is believed that unobserved dark matter is the most likely answer.

There have been other alternatives to all observations, but few can get published since all must meet the publishers criteria of reasonableness, and most of the well-known publishers will not even consider alternatives involving changing-gravity like MOND, or what they consider more speculative models. I have been writing such an alternative-model paper for the last 2 years and hope to get it published in a well-known journal before the end of this year.