The simplest and the best option is to use regular expression and update the string value.
The sample code is as listed below.
partNumberList=partNumberList.replaceAll(":", ":\"").replaceAll("}", "\"}");
The complete code is as shown below
public static void main(String[] args) throws JsonParseException, JsonMappingException,
IOException {
TestJack obj = new TestJack();
//var jsonString ='{"it":"Stati Uniti d'America"}';
// jsonString =jsonString.replace("'", "\\\\u0027")
ObjectMapper mapper = new ObjectMapper();
String partNumberList = "[{productId:AS101R}, {productId:09902007}, {productId:09902002}, {productId:09902005}]";
partNumberList = partNumberList.replaceAll(":", ":\"").replaceAll("}", "\"}");
System.out.println(partNumberList);
mapper.configure(com.fasterxml.jackson.core.JsonParser.Feature.ALLOW_UNQUOTED_FIELD_NAMES, true);
List<ProductDto> jsonToPersonList = null;
jsonToPersonList = mapper.readValue(partNumberList, new TypeReference<List<ProductDto>>() {
});
System.out.println(jsonToPersonList);
}