Creating a full-fledged custom version control system using Amazon S3 versioning requires significant effort and design, including version management, conflict resolution, and user access control. Below, is a simplified C++ program that demonstrates basic functionality for managing different versions of objects in an S3 bucket using the AWS SDK. This program will cover version creation, listing, and retrieval.

Before using this code, make sure to set up the AWS SDK for C++ and configure your AWS credentials. This example does not include conflict resolution or advanced features typically found in version control systems.

#include <aws/core/Aws.h>
#include <aws/s3/S3Client.h>
#include <aws/s3/model/PutObjectRequest.h>
#include <aws/s3/model/ListObjectVersionsRequest.h>
#include <aws/s3/model/ListObjectVersionsOutcome.h>
#include <aws/s3/model/GetObjectRequest.h>

void initializeAwsSdk() {
    Aws::SDKOptions options;
    Aws::InitAPI(options);
}

void shutdownAwsSdk() {
    Aws::ShutdownAPI({});
}

void uploadObjectVersion(const Aws::String& bucketName, const Aws::String& objectKey, const Aws::String& objectData) {
    Aws::S3::S3Client s3Client;

    Aws::S3::Model::PutObjectRequest request;
    request.WithBucket(bucketName).WithKey(objectKey).WithBody(Aws::MakeShared<Aws::StringStream>("CustomVersionControlSystem", objectData));
    auto outcome = s3Client.PutObject(request);

    if (outcome.IsSuccess()) {
        std::cout << "Uploaded a new version of object: " << objectKey << std::endl;
    } else {
        std::cout << "Failed to upload object version: " << outcome.GetError().GetMessage() << std::endl;
    }
}

void listObjectVersions(const Aws::String& bucketName, const Aws::String& objectKey) {
    Aws::S3::S3Client s3Client;

    Aws::S3::Model::ListObjectVersionsRequest request;
    request.WithBucket(bucketName).WithPrefix(objectKey);

    auto outcome = s3Client.ListObjectVersions(request);

    if (outcome.IsSuccess()) {
        const auto& versions = outcome.GetResult().GetVersions();

        std::cout << "Object versions:" << std::endl;
        for (const auto& version : versions) {
            std::cout << "Version ID: " << version.GetVersionId() << std::endl;
            std::cout << "Last modified: " << version.GetLastModified().ToGmtString() << std::endl;
            std::cout << "IsLatest: " << (version.GetIsLatest() ? "Yes" : "No") << std::endl;
            std::cout << "---------------------------------------" << std::endl;
        }
    } else {
        std::cout << "Failed to list object versions: " << outcome.GetError().GetMessage() << std::endl;
    }
}

void retrieveObjectVersion(const Aws::String& bucketName, const Aws::String& objectKey, const Aws::String& versionId) {
    Aws::S3::S3Client s3Client;

    Aws::S3::Model::GetObjectRequest request;
    request.WithBucket(bucketName).WithKey(objectKey).WithVersionId(versionId);

    auto outcome = s3Client.GetObject(request);

    if (outcome.IsSuccess()) {
        Aws::IOStream& objectData = outcome.GetResultWithOwnership().GetBody();
        std::cout << "Retrieved object version content: " << std::endl;
        std::cout << objectData.rdbuf() << std::endl;
    } else {
        std::cout << "Failed to retrieve object version: " << outcome.GetError().GetMessage() << std::endl;
    }
}

int main() {
    initializeAwsSdk();

    Aws::String bucketName = "your-s3-bucket-name";
    Aws::String objectKey = "sample-object-key";
    Aws::String objectData = "This is the content of the object.";

    // Upload object versions
    uploadObjectVersion(bucketName, objectKey, objectData);
    uploadObjectVersion(bucketName, objectKey, "Updated content of the object.");

    // List object versions
    listObjectVersions(bucketName, objectKey);

    // Retrieve an object version
    retrieveObjectVersion(bucketName, objectKey, "your-version-id");

    shutdownAwsSdk();
    return 0;
}

This program initializes the AWS SDK, uploads two versions of an object, lists object versions, and retrieves a specific version by version ID. Remember to replace `your-s3-bucket-name` with your actual S3 bucket name and provide the correct version ID when retrieving an object version.