how SameSite attribute added to my Asp.net_SessionID cookie automatically?

Add these options to web.config for sameSite=None , Lax or Strict

<system.web>
    <httpCookies sameSite="None"/>
    <sessionState cookieSameSite="None" />
    <authentication mode="Forms">
        <forms cookieSameSite="None" />
    </authentication>

CookieSameSite attribute is not available for many older frameworks. If you're in the situation where the accepted answer is not supported in your environment, read on!

I modified upon several SO answers to come up with this URL rewrite that adds SameSite=None to session cookies, and also remove SameSite=None from all cookies for most incompatible browsers. The aim of this rewrite is to preserve the "legacy" behaviour pre-Chrome 80.

Full write-up in my Coder Frontline blog:

<rewrite>
  <outboundRules>
    <preConditions>
      <!-- Checks User Agent to identify browsers incompatible with SameSite=None -->
      <preCondition name="IncompatibleWithSameSiteNone" logicalGrouping="MatchAny">
        <add input="{HTTP_USER_AGENT}" pattern="(CPU iPhone OS 12)|(iPad; CPU OS 12)" />
        <add input="{HTTP_USER_AGENT}" pattern="(Chrome/5)|(Chrome/6)" />
        <add input="{HTTP_USER_AGENT}" pattern="( OS X 10_14).*(Version/).*((Safari)|(KHTML, like Gecko)$)" />
      </preCondition>
    </preConditions>

    <!-- Adds or changes SameSite to None for the session cookie -->
    <!-- Note that secure header is also required by Chrome and should not be added here -->
    <rule name="SessionCookieAddNoneHeader">
      <match serverVariable="RESPONSE_Set-Cookie" pattern="(.*ASP.NET_SessionId.*)" />
      <!-- Use this regex if your OS/framework/app adds SameSite=Lax automatically to the end of the cookie -->
      <!-- <match serverVariable="RESPONSE_Set-Cookie" pattern="((.*)(ASP.NET_SessionId)(=.*))(?=SameSite)" /> -->
      <action type="Rewrite" value="{R:1}; SameSite=None" />
    </rule>

    <!-- Removes SameSite=None header from all cookies, for most incompatible browsers -->
    <rule name="CookieRemoveSameSiteNone" preCondition="IncompatibleWithSameSiteNone">
      <match serverVariable="RESPONSE_Set-Cookie" pattern="(.*)(SameSite=None)" />
      <action type="Rewrite" value="{R:1}" />
    </rule>
  </outboundRules>
</rewrite>

This should work for most ASP .Net and ASP .Net Core applications, although newer Frameworks have proper code and config options to let you control this behaviour. I would recommend researching all the options available to you before using my rewrite above.