You can fetch product attribute options details by REST API with endpoint V1/products/attributes/:attributeCode/options in Magento.
To Access Product Attribute Options, you must have access to the given Role permission,
<resource ref="Magento_Catalog::attributes_attributes" />
You must also need to generate an Admin Token value to pass in the header of the API Call.
Action: GET
URL: <WEBSITE_URL>/rest/V1/products/attributes/:attributeCode/options
(Example: https://mage245.test/rest/V1/products/attributes/color/options)
Header: Authorization Bearer <ADMIN_TOKEN>
Payload: Empty
Response: Array of options label value pair.
Sample Response for the Product Attribute Color,
[
{
"label": " ",
"value": ""
},
{
"label": "Black",
"value": "49"
},
{
"label": "Blue",
"value": "50"
},
{
"label": "Brown",
"value": "51"
},
{
"label": "Gray",
"value": "52"
},
{
"label": "Green",
"value": "53"
},
{
"label": "Lavender",
"value": "54"
},
{
"label": "Multi",
"value": "55"
},
{
"label": "Orange",
"value": "56"
},
{
"label": "Purple",
"value": "57"
},
{
"label": "Red",
"value": "58"
},
{
"label": "White",
"value": "59"
},
{
"label": "Yellow",
"value": "60"
}
]