Assuming you mean the Confluent Kafka REST Proxy since Apache Kafka does not have a REST API for consuming messages.
Full docs are on the Confluent web site here
https://docs.confluent.io/current/kafka-rest/docs/api.html
Version 0.10 is the version of Apache Kafka but not the version of the Confluent REST Proxy. The Confluent release that includes Apache Kafka 0.10.0 is Confluent 3.0.0. There are many enhancements to the REST Proxy since this release several years ago so suggest that you upgrade to 4.0 or 4.1 and use the v2 REST API.
In the newer versions you can POST a list of offsets like this:
POST /consumers/testgroup/instances/my_consumer/offsets HTTP/1.1
Host: proxy-instance.kafkaproxy.example.com
Content-Type: application/vnd.kafka.v2+json
{
"offsets": [
{
"topic": "test",
"partition": 0,
"offset": 20
},
{
"topic": "test",
"partition": 1,
"offset": 30
}
]
}