Action dispatch cookies is responsible for writing cookies to browser set in application, this uses Rack::Utils.set_cookie_header!.
Support for SameSite has been added after rack version 1.6, you need to check your rack version in Gemfile and if it is < 1.6 you need to add the following code in config/initializers
require 'rack/utils'
module Rack
  module Utils
    def self.set_cookie_header!(header, key, value)
      case value
      when Hash
        domain  = "; domain="  + value[:domain] if value[:domain]
        path    = "; path="    + value[:path]   if value[:path]
        max_age = "; max-age=" + value[:max_age] if value[:max_age]
        expires = "; expires=" +
          rfc2822(value[:expires].clone.gmtime) if value[:expires]
        secure = "; secure"  if value[:secure]
        httponly = "; HttpOnly" if value[:httponly]
        same_site =
          case value[:same_site]
          when false, nil
            nil
          when :none, 'None', :None
            '; SameSite=None'
          when :lax, 'Lax', :Lax
            '; SameSite=Lax'
          when true, :strict, 'Strict', :Strict
            '; SameSite=Strict'
          else
            raise ArgumentError, "Invalid SameSite value: #{value[:same_site].inspect}"
          end
        value = value[:value]
      end
      value = [value] unless Array === value
      cookie = escape(key) + "=" +
        value.map { |v| escape v }.join("&") +
        "#{domain}#{path}#{max_age}#{expires}#{secure}#{httponly}#{same_site}"
      case header["Set-Cookie"]
      when nil, ''
        header["Set-Cookie"] = cookie
      when String
        header["Set-Cookie"] = [header["Set-Cookie"], cookie].join("\n")
      when Array
        header["Set-Cookie"] = (header["Set-Cookie"] + [cookie]).join("\n")
      end
      nil
    end
  end
end
Once done you can set SameSite attribute while creating a new cookie, for ex:
cookies['testing'] = {
  value: 'test',
  path: '/',
  expiry: 1.weeks.from_now,
  same_site: :none
}
you can also add the same_site: <value> to your session store as well.
Hope this helps!