OWC sells an external enclosure for the original Apple SSD you remove from your laptop. Last year people using third party SSDs (including OWC) were unable to upgrade macOS due to firmware issues and the only fix at the time was to install HS or Mojave to an original Apple SSD first so the system firmware was updated. Those are also the only third party SSDs with any official support behind them when used with a Mac. You do have to be careful as one of the Aura SSDs requires OSX 10.13+ High Sierra to be used or the SSD won't be recognized. The only option for an internal third party SSD without the use of an adapter is the OWC Aura SSDs which mentions. You will need to do more thorough research before choosing this option. To find the SSD for your model, choose your model from the drop down list below.

I do know that some Samsung SSDs are not compatible with a Mac, but I don't know which ones. We carry replacement SSDs for all Macbook, Macbook Pro, and Macbook Air models. APO/FPO, Afghanistan, Africa, Alaska/Hawaii, American Samoa, Anguilla, Antigua and Barbuda, Armenia, Aruba, Azerbaijan Republic, Bahamas, Bahrain, Bangladesh, Barbados, Belize, Bermuda, Bhutan, Bolivia, British Virgin Islands, Brunei Darussalam, Cayman Islands, China, Cook Islands, Costa Rica, Dominica, Dominican Republic, Ecuador, El Salvador, Falkland Islands (Islas Malvinas), Fiji, France, French Guiana, French Polynesia, Georgia, Germany, Gibraltar, Greenland, Grenada, Guadeloupe, Guam, Guatemala, Guernsey, Guyana, Haiti, Honduras, Iceland, Iraq, Jamaica, Jersey, Jordan, Kazakhstan, Kiribati, Kuwait, Kyrgyzstan, Lebanon, Macau, Maldives, Marshall Islands, Martinique, Micronesia, Mongolia, Montserrat, Nauru, Nepal, Netherlands Antilles, New Caledonia, Nicaragua, Niue, Norway, Oman, Pakistan, Palau, Panama, Papua New Guinea, Paraguay, Peru, Russian Federation, Saint Kitts-Nevis, Saint Lucia, Saint Pierre and Miquelon, Saint Vincent and the Grenadines, Solomon Islands, Sri Lanka, Suriname, Svalbard and Jan Mayen, Taiwan, Tajikistan, Tonga, Trinidad and Tobago, Turkmenistan, Turks and Caicos Islands, Tuvalu, Ukraine, Uzbekistan, Vanuatu, Vatican City State, Venezuela, Virgin Islands (U.S.I know some people on these forums have used a Sintech adapter to use a standard M.2 SSD, but I believe you have to be careful which one you get.

Macbook air 2013 ssd upgrade